# Machine Learning-guided accelerated discovery of structure-property
correlations in lean magnesium alloys for biomedical applications

Sreenivas Raguraman<EMAIL_ADDRESS>Maitreyee Sharma Priyadarshini  Tram
Nguyen  Ryan McGovern  Andrew Kim  Adam J. Griebel  Paulette Clancy  Timothy
P. Weihs<EMAIL_ADDRESS>
###### Abstract

Magnesium alloys are emerging as promising alternatives to traditional
orthopedic implant materials thanks to their biodegradability,
biocompatibility, and impressive mechanical characteristics. However, their
rapid in-vivo degradation presents challenges, notably in upholding mechanical
integrity over time. This study investigates the impact of high-temperature
thermal processing on the mechanical and degradation attributes of a lean Mg-
Zn-Ca-Mn alloy, ZX10. Utilizing rapid, cost-efficient characterization methods
like X-ray diffraction and optical, we swiftly examine microstructural changes
post-thermal treatment. Employing Pearson correlation coefficient analysis, we
unveil the relationship between microstructural properties and critical
targets (properties): hardness and corrosion resistance. Additionally,
leveraging the least absolute shrinkage and selection operator (LASSO), we
pinpoint the dominant microstructural factors among closely correlated
variables. Our findings underscore the significant role of grain size
refinement in strengthening and the predominance of the ternary Ca2Mg6Zn3
phase in corrosion behavior. This suggests that achieving an optimal blend of
strength and corrosion resistance is attainable through fine grains and
reduced concentration of ternary phases. This thorough investigation furnishes
valuable insights into the intricate interplay of processing, structure, and
properties in magnesium alloys, thereby advancing the development of superior
biodegradable implant materials.

###### keywords:

magnesium alloys , machine learning , corrosion , mechanical properties ,
rapid characterization

††journal: arXiV

[inst1]organization=Department of Materials Science and Engineering, Johns
Hopkins University,addressline=3400 N Charles St, city=Baltimore,
postcode=21218, state=MD, country=U.S.A

[inst2]organization=Hopkins Extreme Materials Institute, Johns Hopkins
University,addressline=3400 N Charles St, city=Baltimore, postcode=21218,
state=MD, country=U.S.A

[inst3]organization=Department of Chemical and Biomolecular Engineering, Johns
Hopkins University,addressline=3400 N Charles St, city=Baltimore,
postcode=21218, state=MD, country=U.S.A

[inst4]organization=Translational Tissue Engineering Center, Johns Hopkins
School of Medicine,addressline=400 N Broadway, city=Baltimore, postcode=21231,
state=MD, country=U.S.A

[inst5]organization=Department of Biomedical Engineering, Johns Hopkins
University,addressline=3400 N Charles St, city=Baltimore, postcode=21218,
state=MD, country=U.S.A

[inst6]organization=Research and Development, Fort Wayne Metals Research
Products Corp,addressline=9609 Ardmore Ave, city=Fort Wayne, postcode=46809,
state=IN, country=U.S.A

[inst8]organization=Department of Mechanical Engineering, Johns Hopkins
University, addressline=3400 N Charles St, city=Baltimore, postcode=21218,
state=MD, country=U.S.A

##  1 Introduction

Biodegradable magnesium alloys have emerged as a cutting-edge focus of modern
materials science and biomedical engineering due to their exceptional
mechanical properties and innate ability to degrade within the human body.
These attributes make them a compelling choice for medical implants. [1, 2]
However, to fully harness the potential of biodegradable magnesium alloys, we
must gain a comprehensive understanding of how their microstructure changes
with thermal treatment and how these transformations affect their mechanical
and corrosion properties. [3, 4, 5] In the context of biodegradable magnesium
alloys, striking the right balance between corrosion resistance and
deformation resistance becomes all the more critical. These alloys must endure
mechanical stresses in their intended applications while gradually degrading
as new tissue forms. Achieving this balance is a substantial challenge, as
pure magnesium is renowned for its excellent biocompatibility but is
susceptible to deformation and rapid corrosion. One standard method to enhance
the properties of magnesium is to introduce alloying elements that stimulate
the formation of secondary phases. These secondary phases substantially
improve the material’s mechanical strength, but often at the cost of reduced
corrosion resistance, a trade-off of particular relevance to biodegradable
magnesium alloys. [6, 7, 8] Given the growing interest in developing magnesium
alloys for biomedical purposes, exemplified by the recent FDA approval of the
RemeOS screw [9], a deeper understanding of the intricate interplay between
microstructural features and material properties is of utmost importance.

The impact of microstructural features on material properties is often
quantified using sophisticated characterization tools such as TEM, which
imposes not only substantial financial costs but also consumes considerable
time. In response to these challenges, this study harnesses the power of lab-
based X-ray diffraction and optical microscopy to rapidly characterize
essential microstructural parameters such as dislocation density,
crystallographic texture, intermetallic phase fraction, and grain size for a
given Mg alloy.

One of the significant challenges in identifying the impact of individual
microstructural features lies in their interdependence; they are not isolated
entities but rather highly correlated. [10, 11] This can be illustrated by the
example of Zener particle-pinning [12], in which grain growth is hindered by
secondary phases located on grain boundaries. While the restriction of grain
growth by the particles enhances hardness and strength, the particles can also
accelerate corrosion. Comprehending and untangling the individual effects of
these highly correlated features is difficult.

Figure 1: Schematic illustrating the methodologies employed for understanding
process-structure-property relationships, including accelerated
characterization via XRD and optical microscopy, expedited property assessment
through hardness measurements and 1-day immersion studies, and application of
machine learning techniques such as Pearson Correlation Coefficient (PCC)
analyses [13] and LASSO [14] for comprehending structure-property
correlations.

Recent advancements in machine learning algorithms have guided a new era of
exploration, allowing for an in-depth analysis of individual parameters and
the identification of dominant factors that significantly influence properties
of interest, as evidenced by numerous studies. [15, 16, 17] However, most of
these investigations have either relied on computationally generated data
obtained through calculations or have drawn from experimental data sets
scattered across various sources in the literature, lacking a direct one-to-
one comparison. Furthermore, many of these studies have concentrated on the
chemistry of alloys, with limited attention given to the impact of processing
and microstructural features. Recognizing this gap in the literature, our
study aims to identify the complex relationships between microstructure,
mechanical properties, and corrosion resistance as the microstructure evolves
in a dilute biodegradable magnesium alloy, ZX10, as it is heat-treated over a
broad range of times at 450 °C. Our study documents the evolution of
microstructure, hardness, and in-vitro corrosion rates and identifies the
dominant microstructural features during different stages of the heat
treatment through machine learning, as displayed schematically in Figure 1.

To achieve this, we initiated a simple investigation on a dilute biodegradable
magnesium alloy, ZX10, heat-treated over a broad range of times at 450 °C. Our
study documents the evolution of microstructure, hardness, and in-vitro
corrosion rates and identifies the dominant microstructural features during
different stages of the heat treatment through machine learning, as displayed
schematically in Figure 1.

##  2 Materials and methods

###  2.1 Thermomechanical Processing

The ZX10 quaternary alloy, consisting of high-purity Mg and small
concentrations of Zn (1 wt%), Ca (0.3 wt%), and Mn (0.15 wt%), was synthesized
through a multi-step process. Initially, ingots were created by melting the
constituent elements, followed by a homogenization. The ingots were then
conventionally extruded at 350°C, using an extrusion ratio of 25:1, resulting
in cylindrical rods with a diameter of $\approx$ 12 mm. The extruded rods
underwent further processing using the continuous Equal Channel Angular
Pressing (cECAP) method, where the extruded rods were subjected to four passes
in the $B_{c}$ route at 300°C, followed by an additional four passes in the
$B_{c}$ route at 200°C through a square die of side 11 mm at an angle of
$120\degree$ generating an equivalent strain of 0.67 per pass, as described in
Davis et al.. [18] Samples processed by cECAP are the starting material for
this study and are hereafter referred to as ‘ECAP’.

Prior to solution heat treatment, samples were precision-cut into 11 by 11 by
1 mm3 sheets using wire electric discharge machining, and the heat-affected
regions were removed by polishing with SiC P4000 sandpaper (sourced from
Allied HighTech) and a final polishing step with 0.05 $\mu$ m Colloidal Silica
Suspension to achieve a mirror-like finish. In addition, ThermoCalc, a
CALPHAD-based program, was utilized to calculate the phase diagram of this
alloy (as seen in LABEL:subfig:phase_diagram). Based on the predicted phase
diagram, the ECAP samples were subjected to solution heat treatment in an
Argon gas environment within a Carbolite Gero HTCR5/95 furnace at 450°C, where
only the $\alpha$-Mg phase is stable. Heat treatments ranged from one minute
to a maximum of 128 hours, followed by rapid quenching in water. Moving
forward, each sample is designated by the duration at 450°C. For instance, a
sample that undergoes a 2-minute solution heat treatment is referred to as “2
min” sample. A temperature versus time profile for the initial heating is
plotted in LABEL:subfig:thermocouple_measurements and shows that samples rise
into the solutionizing region, where no secondary phases are stable, within 10
seconds.

###  2.2 Characterization and Quantification of Microstructural Parameters

To characterize and quantify microstructural features rapidly, we employed
optical microscopy and X-ray diffraction. We also leveraged SEM imaging, SEM-
EDS mapping, and SEM-EBSD mapping to verify the consistency of the rapid
analyses. To examine the ECAPed and annealed microstructures, samples were
etched using a 5% Nital solution (composed of 5% Nitric Acid and 95% methanol)
following the ASTM E 407 standard. [19] Optical microscopy was performed using
a Leica DMi8 Inverted Microscope with LASX software for grain size
visualization. JEOL IT700HR InTouchScopeTM SEM and Thermo Scientific Helios 5
UC Focused Ion Dual Beam were employed for imaging and EDS analysis, with EDS
data analysis conducted using APEX EDS software. Grain sizes were measured
using optical micrographs, scanning electron micrographs, and a MATLAB
program, following the intercept method specified in ASTM E112-13. [20]

The mirror-finish samples were subjected to bulk ion beam milling using a
Leica EM TIC 3X at 5kV and 3mA for 5-minutes before Electron Backscattered
Diffraction (EBSD) studies on a Tescan MIRA 3 GM Field Emission SEM, equipped
with Oxford EBSD detector at voltage of 20 kV. Textural and grain size
analyses for EBSD were carried out using AZteC Crystal Software by Oxford. We
also used AZteC Crystal Software to obtain the Geometrically Necessary
Dislocation (GND) density, based on the Weighted Burgers Vector Method
developed by Wheeler et al. [21] To mitigate the step size influence on GND
measurement and examine relative GND density changes, a constant step size of
0.5 $\mu m$ was employed. The analysis focused on the dislocation density of
Burgers vectors with a magnitude of $\frac{1}{2}[11\overline{2}0]$, and the
GND density was assessed using a $3\times 3$ pixel kernel size.

The SEM-EDS images were initially subjected to thresholding by the Otsu method
[22] to distinguish the precipitates from the matrix based on contrast. The
representative diameter of each precipitate was then computed by averaging its
major and minor axes, which served as the basis for calculating the
precipitate size distribution and area fraction.

X-ray diffraction (XRD) analysis was conducted per the principle of Bragg’s
law [23] using the Malvern Panalytical Aeris powder X-ray diffractometer,
operating at 40 kV and 7.5 mA. The instrument was equipped with a Nickel Beta
Filter and a Cu X-ray source, and data collection was performed using a step
size of 0.0027°. To ensure data quality, scans were repeated three times and
subsequently summed to enhance the signal-to-noise ratio. Data processing,
such as background subtraction, removal of K$\alpha_{2}$ peaks, peak
identification, and peak matching, was accomplished using X’pert HighScore
software.

The Convolutional Multiple Whole Fitting (CMWP) program developed by Ribarik
et al. was employed to determine the average dislocation density. The standard
reference material (SRM 660, LaB6) from the National Institute of Standards
and Technology was employed to obtain the instrumental profile function. Due
to very minimal alloying content, the broadening of the Mg peaks was assumed
to arise mainly from the strain contributions of the dislocations in the Mg
phase. The CWMP program has been detailed in [24, 25, 26, 27].
Peaks exceeding a minimum threshold of 0.01 counts after background
subtraction were detected and subjected to PseudoVoigt profile fitting using
X’Pert HighScore Software, as detailed in [28]. To address the impact of
texture on intensity, which can arise from preferential precipitation on
specific planes during annealing, multiple peaks with $2\theta$ values
spanning the range of 20-60° were taken into account.

We estimated the volume fraction for each constituent phase by calculating the
ratio of the integrated area corresponding to an individual phase to the sum
of integrated areas for all phases as described in [29] and as illustrated
below:

$V_{f,a}=\dfrac{A_{a}}{A_{a}+A_{b}+A_{c}+A_{d}}$ (1)

For texture characterization, we focused on the prismatic $[10\overline{1}0]$
and $[11\overline{2}0]$ and basal $[0002]$ planes. The degree of texture was
quantified using ratios of the integrated peak areas for prismatic planes
normalized with respect to the basal plane, as follows:

$\dfrac{V_{(10\overline{1}0)}}{V_{(0002)}}=\dfrac{A_{(10\overline{1}0)}}{A_{(0002)}},\hskip
20.0pt\dfrac{V_{(11\overline{2}0)}}{V_{(0002)}}=\dfrac{A_{(11\overline{2}0)}}{A_{(0002)}}$
(2)

###  2.3 Microhardness evaluation

Microhardness measurements were conducted utilizing a 200 gf load on a LECO
AMH55 Hardness Tester. Vickers hardness values were derived from the
indentation size through the ’Cornerstone’ software. Each hardness data point
represents a total of at least ten measurements. In accordance with DIN-ISO
6507 guidelines [30], the micro-indents were spaced at distances equal to six
times the average indent width.

###  2.4 Bio-corrosion Evaluation

The square samples measuring $11\times 11\times 1\,\text{mm}^{3}$ were
polished on all sides with P4000 SiC paper prior to immersion in Earle’s
Balanced Salt Solution at 5% $\text{CO}_{2}$ and a temperature of 37.1°C,
simulating in-vivo conditions for 24 hours. Immersion bio-corrosion tests were
conducted with a sample surface area to solution volume ratio of
$0.2\,\text{mL/mm}^{2}$ per ASTM G31-72 standard [31]. The testing took place
within a Heraeus Heracell CO2 150 incubator. Following the immersion tests,
the corroded samples were treated with a solution composed of
$(200\,\text{g}\,\text{CrO}_{3}+10\,\text{g}\,\text{AgNO}_{3}+20\,\text{g}\,\text{Ba(NO}_{3})_{2}$
dissolved in $1l$ of deionized water, following the guidelines set forth by
ASTM G1 [32] to remove corrosion products. Mass and pH measurements were
acquired before and after the corrosion testing utilizing a weighing scale
(Hanchen Electronic Analytical Balance, 0.1 mg, Digital Scale) and benchtop pH
meter (Accumet AB150, Thermo Fisher Scientific, MA, USA). The pH level was
maintained below 8. The biocorrosion rate of each sample was calculated by the
weight loss measured in an immersion period of 24 hours according to the
equation in [31]:

$\text{Corrosion Rate}=\dfrac{K\times W}{A\times T\times\rho}\hskip
5.0ptmm/yr$ (3)

where $K$ is a constant ($8.76\times 10^{4}$), $W$ is the weight loss in the
unit of gram, $A$ is the exposed sample surface area in the unit of cm2, T is
the time of exposure in the unit of hours, and $\rho$ is the sample density in
the unit of g/cm3. The calculated density of $1.77\pm 00.26$, obtained using a
helium gas pycnometer (Micromeritics AccuPyc II 1340) and a microbalance
(Mettler Toledo Model XS3DU), were employed to estimate corrosion rates. For
this study, we focused on corrosion over a single day, given that corrosion
rates are usually at their highest initially and tend to decrease over time.

###  2.5 Machine Learning-driven Analysis

We apply two machine learning techniques to understand the correlations
between the microstructural features and to identify the most significant
microstructural features that affect the corrosion rate and hardness. To
obtain correlations between the microstructural features, we compute the
Pearson R correlation coefficients (PCC) [13] using the following equation:

$r_{xy}={\frac{\sum_{i=1}^{n}(x_{i}-{\bar{x}})(z_{i}-{\bar{z}})}{{\sqrt{\sum_{i=1}^{n}(x_{i}-{\bar{x}})^{2}}}{\sqrt{\sum_{i=1}^{n}(z_{i}-{\bar{z}})^{2}}}}},$
(4)

where $x$ and $z$ represent two different microstructural features, $x_{i}$
and $z_{i}$ represent data observations for the given microstructural feature,
and $\bar{x}$ and $\bar{z}$ represent the mean of the observations for $x$ and
$z$. The PCC is computed pairwise for the microstructural features and is a
statistical measure of the linear correlation between two data sets. A
positive PCC value indicates that the values $x$ increases as the value of $y$
increases, and a negative PCC indicates that the value of $x$ decreases as the
value of $y$ increases. We also compute the PCC between each microstructural
feature and the targets - hardness and corrosion rate. This analysis provides
an understanding of how each microstructural feature impacts the strengthening
and degradation of the Mg alloy.

Following the correlation analysis, we performed feature selection using
LASSO. [14] LASSO builds a linear model based on the assumption that the model
coefficient vector ($\beta$) is sparse. This implies that only some of the
input variables are selected to create the linear model. The following
objective function is solved by LASSO:

$\min_{\beta\in\mathbb{R}^{p}}\left\\{{\frac{1}{N}}\left\|y-x\beta\right\|_{2}^{2}+\lambda\|\beta\|_{1}\right\\},$
(5)

where $N$ is the number of data points, $\beta$ is the coefficient vector, $x$
represents the microstructural features data, $y$ represents the targets,
hardness, and corrosion rate, and $\lambda$ represents a tunable
hyperparameter that controls the sparsity of our linear model. In our
implementation for this work, we perform a grid search on the $\lambda$
parameter and select the one that gives the highest accuracy model based on
leave-one-out-cross-validation (LOOCV). We use the mean absolute error and R2
score as the accuracy measure for cross-validation.

##  3 Results and Discussion

###  3.1 Variation in Hardness and Corrosion on Solution Heat Treatment

As depicted in Figure 3, the initial minute of heat treatment produces minimal
impact on hardness; however, there was a sharp decrease (by 30%) after
2-minutes. The hardness then stabilized for approximately 30-minutes before
gradually declining, resulting in a cumulative reduction of 50% by 128 hours.
In contrast, the corrosion rate experienced a rapid decline (40%) within the
first minute, stabilized for the subsequent 30-minutes, and then gradually
decreased until a total reduction of 4X was observed at 128 hours. Notably,
such substantial property changes occurring within brief time intervals (1-2
minutes) are unusual.

Figure 3: Evolution in hardness and corrosion rate with time reveals the loss
of strength and reduced corrosion rate over time.

It was intriguing to note the combination of high strength and relatively
favorable corrosion rates in the 1 min sample. This observation suggests that
high-temperature annealing for shorter durations can enhance the corrosion
behavior of heavily deformed samples. These observations also underscore the
remarkable changes in material properties without alterations in chemistry,
emphasizing the critical role of processing on properties. The underlying
mechanisms driving these transformations lie within the microstructure,
underlining the necessity for ongoing monitoring of microstructural changes to
attain optimal material properties.

###  3.2 Tracking material microstructure rapidly following heat treatment

After subjecting the samples to heat treatments and quenching, we rapidly
characterize four critical microstructural features pertinent to hardness and
corrosion using X-ray diffraction (XRD) and optical microscopy (OM) methods,
which offer advantages in terms of minimal sample preparation, time
efficiency, and cost-effectiveness. These features include dislocation
density, crystallographic texture, precipitate volume, and grain size. [33,
34] While the XRD-derived values provide averaged measurements and may not
capture local variations in dislocation densities or increases in particle
size beyond $200$ $nm$, they serve as valuable tools for explaining the
observed fluctuations in mechanical and corrosion properties as depicted in
Figure 3. XRD patterns and optical microstructures of all the conditions are
plotted in Figures 4 and 6, respectively.

Figure 4: Accelerated Microstructural characterization from XRD: a) XRD
patterns revealing the Mg peaks (in linear scale) and presence of precipitates
(in logarithm scale) b) Dislocation density obtained from CMWP analyses
revealing dislocation annihilation and plateauing post-1-minute annealing; c)
Variation in precipitate content obtained from XRD revealing dissolution of
precipitates; Texture ratios from XRD showing the variation of (d)
(10$\overline{1}$0)/(0002) and (e) (11$\overline{2}$0)/(0002) over time.

####  3.2.1 Variation in Dislocation Density

Based on CMWP analyses as demonstrated in Figure 4(b), the ECAP sample has a
high dislocation density exceeding 3$\times 10^{15}$ m-2 but drops tenfold
after just a one-minute exposure to $450\degree$C, indicative of significant
dislocation annihilation. This dramatic drop is supported by EBSD
measurements, as demonstrated by the geometrically necessary dislocation (GND)
density in Figure 5(d). A noteworthy aspect is the consistent log-normal
distribution of GND density within the heat-treated samples.

Previous studies [35, 36, 37] have predominantly examined variations in
dislocation density over longer time scales, typically spanning 20 minutes or
more. Given our study utilizes far shorter time durations, we conducted in-
situ temperature measurements with thermocouples to ensure samples reach the
annealing temperature rapidly, as shown in
LABEL:subfig:thermocouple_measurements. Note that the samples reach the
solutionizing region within 10 seconds, so even a brief one-minute annealing
period provides sufficient exposure to high temperatures for the annihilation
of dislocations.

Figure 5: Microstructural Evolution validation using SEM: a) SEM-EDS Maps
revealing the presence of different precipitates; b) BSE images showing
precipitate dissolution and coarsening over time; c) Variation in area
fraction and mean diameters of precipitates obtained from SEM showing
precipitate dissolution and coarsening over time; d) Log-normal distributions
of GND Density revealing dislocation annihilation and plateauing post-1-minute
annealing validating the trend from XRD; g) EBSD Pole figures revealing the
texture variation over time

####  3.2.2 Crystallographic Texture Evolution

In terms of crystallographic texture, we primarily considered three planes for
our study: the basal $(0002)$ plane and the prismatic $(10\overline{1}0)$ and
$(11\overline{2}0)$ planes, which have been identified as significant
influencers of corrosion behavior as per literature. It is worth noting that
prismatic planes corrode 18-20 times faster than basal planes. [38, 34] Thus,
texture ratios were calculated using integrated areas from XRD scans as
detailed in Section 2.2, and both integrated area ratios
$(10\overline{1}0)/(0002)$ and $(11\overline{2}0)/(0002)$ show similar trends
over time as seen in Figure 4(d) and (e). The XRD intensity of the
$(10\overline{1}0)$ plane remains relatively constant from the first minute
onwards, whereas the intensities of the $(11\overline{2}0)$ and $(0002)$
planes fluctuate in response to the heat treatment duration. The most
pronounced variations occur during the second minute, which coincides with the
onset of grain growth.

The EBSD pole figures reveal a similar trend while offering intriguing
additional insights. The texture notably weakens from the ECAP to the 1-minute
sample. In the ECAP sample, the basal plane texture tilts approximately
$45\degree$ to the normal. Conversely, we observe a wider range of texture
variation in the one-minute sample, spanning from $25\degree$ to $65\degree$
to the normal. However, a significant texture strengthening occurs in the
2-minute sample, with the basal pole aligning more closely towards the center
of the pole figure. As subsequent sections will explain, the dissolution of
precipitates leads to an increase in grain size from 1-minute to 2-minutes,
consequently altering the texture. By the 128-hour mark, the basal texture,
$(0001)$, exhibits a more dispersed pattern, aligning closer to the
$0-45\degree$ range along the x-axis, as illustrated in Figure 5(e).

####  3.2.3 Precipitate Evolution

In this alloy, three common types of precipitates were observed: Ca2Mg6Zn3,
Mg2Ca, and Mn, as evidenced by both XRD (Figure 4(c)) and SEM-EDS analyses
(Figure 5(a-c)). This observation aligns with the predicted phase diagram by
ThermoCalc, illustrated in LABEL:subfig:phase_diagram. At
$450\degree\text{C}$, all three phases are thermodynamically unstable, and the
stable phase is a solid solution. However, solutionizing completely requires
significant time.

While determining phase volume fraction using integrated area measurements
from XRD (Figure 4), the influence of texture on preferential precipitation
was deemed negligible. As expected, the calculated volume fraction of all
three phases decreased with annealing time, as illustrated in Figure
5(b).Within the initial minute of exposure at 450°C, the overall precipitate
fraction decreased by approximately 30%. Subsequently, from 1-2 minutes, there
was a decrease of around 6%, followed by stepwise declines in the precipitate
fraction, each below 1%, until the 4th-hour mark, when more pronounced
decreases occur over time, resulting in close to a 70% reduction in
precipitate content.

While XRD measurements do not provide detailed insights into precipitate size
and distribution, they facilitate the identification of precipitate
dissolution and differential dissolution rates among precipitates, which are
challenging to obtain through optical microscopy or SEM. On the other hand,
SEM-EDS maps provided an understanding of precipitate morphology within its
resolution limit and also confirmed the dissolution of precipitates over time,
corroborating our XRD analyses. Image analysis of backscattered electron (BSE)
images also revealed that precipitate diameter increased over time while area
fraction decreased, as seen in Figure 5(b) and Figure 5(c).

Upon closer examination of individual precipitate variation over time, the
initial drop in precipitate content within the first minute is attributed
primarily to the ternary Ca2Mg6Zn3 phase, exhibiting close to a 40% decrease.
This substantial reduction can be attributed to the high mobility of Zn atoms
in the Mg matrix, as calculated from diffusion coefficient data obtained from
[39]. Zn atoms display a significantly higher interdiffusion coefficient (9.24
$\mu m^{2}/s$) at 450°C compared to Ca atoms (0.19 ${\mu m}^{2}/s$) and Mn
(0.001 ${\mu m}^{2}/s$), as well as Mg’s self-diffusion coefficient (0.03 $\mu
m^{2}/s$). The data also explains the slower dissolution of the Mg2Ca phase
and minimal change in the Mn phase.

The dissolution of precipitates within such short time scales, as observed in
the first minute, appears to be an unexplored phenomenon in past literature.
Most studies [40, 41, 42, 43, 44] typically focus on precipitate evolution
starting at 30-minutes or longer. However, this study underscores the
importance of monitoring microstructural features at smaller time scales,
particularly at elevated temperatures, in part because short processing times
are advantageous to industry.

####  3.2.4 Grain Size Variation

Our investigation into grain size primarily relied on optical microscopy
(Figure 6(a)), complemented by EBSD grain size measurements (Figure 6(b)) at
specific time intervals to validate our findings. Initially, the ECAP samples
exhibited highly refined grains, averaging approximately 800 $nm$ in size.
Despite the observed dislocation annihilation, a one-minute annealing process
did not induce significant changes in grain size. However, as the heat
treatment extended to 128 hours, the grain size increased significantly by
60-fold, reaching nearly 50 $\mu m$ towards the end of the process.

Of particular note is the ten-fold increase in grain size observed from the
first minute to the second minute, a phenomenon also evident in the texture
variations illustrated in Figure 5(e) and 5(i). Such substantial changes in
microstructure tend to be under-reported in the literature that typically
considers longer time periods. [45, 46]

Figure 6: Grain Size Analysis: a) Optical Microstructures revealing grain size
coarsening over time; b) Inverse Pole Figures of ECAP, 1 min, 2 min, and 128
hr samples confirming the rapid grain growth; c) Grain size distributions as a
function of condition revealing abnormal grain growth; d) The variation in the
width of grain diameter over time, and the fit as per Equation 6 denoting the
abnormal grain growth; e) Variation in 3D grain radius as a function of time,
with a fit per the Zener model (Equation 7) revealing the abnormal grain
growth in the 2nd min and 5th min samples, beyond which the grain growth is
normal.

To understand this rise in grain growth behavior, we employed the well-
established grain growth model [11]:

$d^{n}+d_{o}^{n}=kt,$ (6)

where $k$ is the grain growth exponent, $t$ is the time, $d_{o}$ is the
initial grain size, and $d$ is the grain size at time, $t$. Fitting the model
yields a grain growth exponent, $n\approx 5.5$, that is a substantial
deviation from the value proposed by Burke and Turnbull (n = 2) [47] as seen
in Figure 6(d). This deviation points to the occurrence of abnormal grain
growth, a phenomenon characterized by the sudden emergence of unusually large
grains within a matrix of uniformly sized grains. An analysis in Supplementary
Table SI 1 reveals the presence of island grains, characterized by grains with
double the average grain size, a characteristic feature of abnormal grain
size. This phenomenon is not uncommon and has been well-documented in previous
studies in magnesium alloys. [45, 48, 11, 49] The grain growth exponent
observed in this study is consistent with findings from these previous
studies, where $n$ typically falls within the range of 2 to 7.

This grain growth model assumes boundary curvature drives growth, the absence
of a drag force on the boundary due to particles or solutes, and isotropic
grain boundary energies and mobilities. Given this alloy contains second-phase
particles, we investigated grain size distributions over time, which revealed
deviations from self-similarity, a hallmark of abnormal grain growth as
described by Humphreys [12] and seen in Figure 6(c). A high value of $n$
points to grain growth stagnation, likely due to second-phase particles
exerting a drag force on the boundaries, effectively pinning the
microstructure. As illustrated in Supplementary Figure 9, the normalized grain
distribution and the variation in the width of the normalized distribution
exhibit specific patterns. The normalized grain size distributions remain log-
normal throughout, except in the 2 min sample as revealed in Supplementary
Table SI 2. Notably, the breadth of the distribution does not change
significantly under any of the annealing conditions; instead, it oscillates.
This observation suggests that while some grains began growing at a much
faster rate than others, broadening the distribution, the finer grains rapidly
caught up, preventing distributions from becoming bimodal. [48, 11] This
transient nature of abnormal grain growth has been observed in previous
experiments and simulations. [47, 50, 51, 52, 12]

The most commonly cited explanation for abnormal grain growth revolves around
the coarsening of particles that effectively pin the grain boundaries, as
explained well in [11]. The classical approach to understanding the impact of
pinning particles on grain growth is to employ the Zener model [53]:

$R_{c}=\frac{4r}{3f},$ (7)

where $R_{c}$ is the limiting grain radius, $r$ is the radius of the pinning
particles, and $f$ is the volume fraction of the particles. This equation,
while based on several simplifying assumptions like spherical particles and
grains and randomly distributed particles with no preferential arrangement at
grain boundaries, has been applied here to provide a semi-quantitative
comparison between observed and predicted grain sizes.

Our observations (Figure 6(e)) indicate that in the ECAP and 1-minute samples,
the observed grain radius remains significantly below the calculated critical
radius, hereafter referred to as the Zener radius. There appear to be two
distinct regions of normal grain growth separated by a segment of abnormal
grain growth (2 min and 5 min): the first region encompasses ECAP and
1-minute, and the second region starts from 15-minutes all the way to 128
hours, aligning with the trend visible in the grain size distribution plot in
Figure 6(d).

This unusual behavior in the 2-minute sample is attributed to the significant
dissolution of the ternary phases in the first minute, which leads to an
approximately ten-fold increase in average grain size. Since these ternary
particles may be heterogeneous in size and distribution, pinning of grain
boundaries and grain growth may also be heterogeneous, resulting in a bimodal
distribution as revealed in Supplementary Table SI 2. However, by 5-minutes,
many of these particles dissolve, contributing to a nearly 8-fold rise in
grain size from 2-5 minutes and log-normal distributions of grain sizes.
Subsequently, the grain growth stabilizes and follows normal grain growth
behavior. This study reveals the highly correlated nature of microstructural
features, wherein the presence of secondary phases correlates with and appears
to control grain growth and texture evolution.

###  3.3 Correlations between Microstructural Features

Figure 7: Correlations between the microstructural features (a) with ECAP and
(b) without ECAP sample.

Figure 7 displays the Pearson R correlation coefficients (PCC) [13] for the
microstructural features characterized in our study. The left matrix in Figure
7(a) presents results obtained while including the ECAP sample before any
solution treatment, while the right matrix Figure 7(b) shows correlation
coefficients after excluding data for the ECAP sample.

Upon removing the ECAP sample point, significant changes in correlations are
evident, particularly regarding the dislocation density, $\rho$. This
variation can be attributed to dislocation annihilation occurring during the
initial minute of high-temperature annealing, as detailed in Section 3.2.1 and
Figure 4(b). The sudden initial drop in dislocation density results in the
identification of some unusual and unphysical correlations, such as between
dislocation density and ($11\bar{2}0/0002$) texture ratio. Additionally, the
dislocation density exhibits small positive correlations with precipitate
volume fractions. This may arise from the simultaneous occurrence of
dislocation annihilation and precipitate dissolution upon annealing, leading
to these unexpected correlations.

Our analysis in Figure 7(b) reveals a strong negative correlation between
grain size ($d$) and precipitate volume fractions, consistent with Zener
theory (Equation 7). Furthermore, grain size exhibits a robust negative
correlation with texture for the ($11\bar{2}0/0002$) texture ratio, which
could explain the observed trend of the texture becoming more basal over time,
as depicted in the pole figures in Figure 5(e). Moreover, we observe high
correlations among the three precipitate volume fractions, which is
unsurprising given their relationship through the constraint that their sum
equals 1. This correlation likely arises from the simultaneous dissolution of
all these precipitates over time.

The correlations presented here offer valuable insights into the interplay
between various microstructural features in our alloy system, shedding light
on the complex relationships governing its behavior. Taken together, the data
underscores the importance of accelerated characterization combined with
advanced statistical analysis in understanding such correlations.

###  3.4 Machine Learning-guided Structure Property Correlations

####  3.4.1 Strengthening Mechanism

In this investigation, we utilize a machine learning approach comprising
Pearson correlation coefficient [13] and LASSO regression [14] analyses to
understand the influence of individual microstructural features on hardness.
Recognizing the limitations posed by a small dataset, we address this
challenge by integrating established physics-based models for strengthening
into these feature selection models. This integration involves leveraging
physics-based features, a strategy detailed below.

In general, the common physical factors contributing to the strengthening of a
magnesium alloy are solid solution strengthening ($\sigma_{SS}$), dislocation
strengthening ($\sigma_{dis}$), grain size strengthening ($\sigma_{gb}$), and
precipitation strengthening ($\sigma_{ppt}$). Based on previously known
theory, we can estimate the total strengthening in the alloys to be a sum of
individual strengthening mechanisms. [54]

$\displaystyle\sigma$ $\displaystyle=$
$\displaystyle\sigma_{SS}+\sigma_{Dis}+\sigma_{GB}+\sigma_{ppt},$
$\displaystyle=$ $\displaystyle m\sum_{i}B_{i}(X_{i})^{2/3}+M\alpha
Gb\sqrt{\rho}+kd^{-1/2}+\Delta\tau.$

In Equation 3.4.1, the first term represents the contribution from solid
solution strengthening as explained by the Labusch model [55, 56], the second
term represents the contribution from dislocations that can be estimated by
[54], the third term represents grain boundary strengthening based on the
Hall-Petch relationship [57], and the last term represents the contribution
from precipitates as estimated using the Orowan model. [54] The individual
fits of each of these models are listed in the A.6.

For solution-strengthening, $X_{i}$ denotes the atomic fraction of solute $i$,
and $B_{i}$ represents the potency factor corresponding to solute element $i$.
Assuming all the solute atoms ($0.4$ at.% of Zn and $0.2$ at.% of Ca) are in
solution, the maximum solution-hardening is estimated to be only $10$ MPa /
$3.3$ HV (calculated from [58]). We neglect the contribution of Mn due to its
minimal content ($<0.07$ at.%). Since this maximum hardening is barely 1% of
the measured hardness, we consider solid solution-strengthening to be
negligible and do not consider it for the analyses. In Equation 3.4.1, the
parameter $\alpha=0.2$ captures dislocation interactions within the basal slip
system, $G$ signifies the shear modulus of the Mg matrix (approximately
$16.6\,\text{GPa}$), $\rho$ encapsulates dislocation density, $b$ represents
the Burgers vector (roughly $0.32\,\text{nm}$), $M$ is the Taylor factor
($\approx 4.5$ in Mg alloys [59]), $d$ signifies the grain size, $k$ is the
Hall-Petch slope obtained by fitting our data into the above model, and
$\Delta\tau$ is the increment in the critical resolved shear stress (CRSS) due
to precipitates. [60] To quantify the strengthening effect of precipitates,
the increment in the $\Delta\tau$, resulting from the necessity for
dislocations to bypass two distinct precipitates, is estimated as follows:

$\Delta\tau=\dfrac{Gb}{2\pi\lambda^{*}\sqrt{1-\nu}}\ln{\dfrac{d_{p_{i}}^{*}}{r_{o}}}.$
(9)

Here, $\lambda^{*}$ signifies the effective planar inter-particle spacing on
the slip plane, $\nu$ is the Poisson’s ratio of the Mg matrix ($\approx 0.3$),
$d_{p_{i}}^{*}$ denotes the mean planar diameter of the particles on the slip
plane calculated from XRD using the Scherrer equation and assuming that peak
broadening is due to particle size effects. $r_{o}$ is the core radius of the
dislocations, approximated to be the magnitude of $b$ ($r_{0}=0.32\,nm$). [61]
Given the Scherrer equation is only valid for particle sizes less than 200 nm
[62], we limit our consideration to particles below this threshold, which are
the ones most responsible for strengthening. Following the methodology
outlined by J.F. Nie [63], the mean inter-precipitate spacing can be
approximated based on the volume fraction of the precipitates, $f$ and mean
diameter of the precipitates, $d_{p_{i}}^{*}$ as:

$\lambda=(\dfrac{0.779}{\sqrt{f}}-0.785)\times d_{p_{i}}^{*}.$ (10)

The precipitate size and spacing obtained through this route are listed in the
Table SI 3. We carried out hardness (H${}_{\text{V}}$) to yield strength
($\sigma_{y}$) conversions using the relationship where ($\sigma_{y}\approx
3.3\times\text{H}_{\text{V}}$). [64] Given the absence of existing models
describing the influence of texture on strength, we opted to utilize the
texture intensity ratios derived directly from XRD.

Using the above relations, we first conducted a correlation analysis using the
Pearson R correlation coefficients [13] between the microstructural features
and the hardness value as seen in LABEL:subfig:hardness_pcc. We observed that
the inverse square root of the mean grain size ($1/\sqrt{d}$) is strongly
positively correlated with hardness, implying that the hardness value
increases with a decrease in the grain size, consistent with Hall-Petch
strengthening. [57] Likewise, the descriptors for precipitates in both ternary
and binary phases exhibit a positive correlation with hardness values,
suggesting that the presence of precipitates enhances alloy hardness, as
anticipated in precipitation strengthening. [54, 40] This correlation may also
be due to precipitates hindering grain growth rather than directly resulting
from precipitation strengthening.

However, the unusual, highly positive correlation observed with
($11\overline{2}0/0002$) texture ratio and its impact on hardness could stem
from its significant decrease over time. Similarly, the very slight negative
correlation seen with ($10\overline{1}0/0002$) texture ratio might result from
the relatively constant intensity of ($11\overline{2}0$) plane during
annealing, coupled with changes primarily in ($0002$) plane. Although both
textures exhibit correlations, these are indirect and do not directly affect
hardness, as indicated by LASSO descriptors below and previous literature.
Instead, it’s the precipitates influencing grain growth that effectively
impact texture as elaborated in Section 3.2.2.

As correlations do not imply causation, we conducted LASSO regression to
further understand the importance and dominance of microstructural features.
LASSO, a method known for its ability to simplify models by eliminating less
impactful variables, provided a refined understanding of the most significant
features affecting hardness. Our LASSO model estimated the contribution and
dominance of each feature using physics-informed and microstructure-based
models, as seen below:

$\displaystyle H_{V}$ $\displaystyle=$
$\displaystyle\lambda[A(1/\sqrt{d})+B\sqrt{\rho}+\sum_{i}C_{i}(\frac{1}{\lambda^{*}}ln[d_{0}])+...$
(11) $\displaystyle...$
$\displaystyle+D\frac{(10\overline{1}0)}{(0002)}+E\frac{(11\overline{2}0)}{(0002)}],$

where A, B, $C_{i}$, D, and E are fitting constants in LASSO that give the
feature importance value. The LASSO regression fit has an accuracy of 93.14%,
and the fit was obtained by optimizing over the $\lambda$ parameter using
“leave-one-out”-cross-validation (LOOCV).

In LABEL:subfig:hardness_lasso, our analysis underscores the predominant
influence of grain size on the mechanical properties of the materials studied,
aligning with established literature on the dominance of grain size
strengthening in Magnesium alloys. [65, 66, 67] This phenomenon arises from
the hindrance of dislocation and twinning motion by grain boundaries, which
enhances the yield strength within the Mg matrix. The Hall-Petch slope ($k$),
ranging from 90 to 300 MPa $\mu m^{1/2}$, surpasses that of Al alloys or Steel
by a factor of 2-5, highlighting the significance of grain size in
strengthening. [67, 57]

While both ternary and binary precipitates contribute to material
strengthening, our analysis suggests that the ternary phase plays a relatively
more substantial role in accordance with experimental observations. This could
result from the higher volume fraction of the ternary phase over the binary
phase. Despite their positive correlation with hardness, the impact of
precipitates on strengthening, as inferred from LASSO analysis, appears
comparatively modest. This observation aligns with the limited effectiveness
of precipitates in strengthening via the Orowan mechanism [40], likely due to
their susceptibility to cutting by dislocations. [68, 67] Additionally, in the
context of a dilute alloy system, the effectiveness of precipitates in
strengthening is further compromised. The tendency for coarsening and
dissolution of precipitates over time leads to diminished strengthening
effects, as confirmed by LASSO analysis. The relative influence of
precipitates on strength is largely dictated by their volume fraction, with
the ternary phase exhibiting the highest importance, followed by binary
precipitates, and then the Mn phase with its extremely low volume fraction.
However, it is worth noting that precipitates indirectly contribute to
strengthening by impeding grain growth during solution treatment, thereby
enhancing strength through the Hall-Petch mechanism. This explains the
discrepancy between the high correlation observed through Pearson R
Correlation and the relatively lower importance assigned by LASSO analysis.

In contrast, dislocation strengthening does not feature prominently in our
analysis despite its high correlation with hardness. This discrepancy arises
from the significant drop in dislocation density during the initial phase of
high-temperature solution treatment, followed by stabilization at relatively
constant levels. However, lower temperature annealing regimes may reveal a
more pronounced impact of dislocations on hardness, as indicated by PCC
analysis. [54]

When considering other microstructural features, the contribution of texture
to strengthening appears negligible, likely due to its minimal influence on
hardness. This observation is consistent with prior research highlighting the
limited effect of texture on material hardness. [69, 70]

####  3.4.2 Corrosion Mechanism

Corrosion rates in Mg alloys, much like strengthening, are influenced by
various microstructural factors, including grain size, secondary phases,
texture, and dislocation. However, there remains a gap in theoretical models
linking these microstructural features to corrosion rates. Only a few studies
have attempted to establish such correlations [71, 72].

In line with methodologies used for understanding strengthening mechanisms, we
employ Pearson correlation analysis [13] and LASSO regression techniques [14]
to assess the influence of individual microstructural features on corrosion
rate. To mitigate the limitations posed by a relatively small dataset, we
integrate established physics-based models for strengthening into the feature
selection process of both Pearson correlation coefficient (PCC) and LASSO
regression models, as elaborated below.

Grain size ($d$) is one of the most critical microstructural features
influencing corrosion rate. Given that grain boundaries harbor more lattice
defects and dislocations compared to the interiors of grains, grain boundaries
are expected to corrode faster when exposed to corrosive environments. As a
result, grain boundaries are considered to accelerate the corrosion rate.
However, the relationship between grain size and the corrosion rate is
complex, with conflicting reports suggesting that larger or smaller grain
sizes may either decrease or elevate the corrosion rates. [73, 3, 74, 34, 75]

Here we utilize the Hall-Petch type model that Ralston and Birbilis proposed
to explain the relationship between corrosion rate and grain size [71]:

$CR=A+\dfrac{B}{\sqrt{d}}.$ (12)

where the constant $A$ depends on the specific environmental conditions, and
$B$ represents a material constant that varies with composition. The fit of
the Ralston-Birbilis model is listed in Supplementary Figure SI 6. A modified
version of the Ralston-Birbilis model was proposed by Bahmani et al. [75],
where the grain size effect is limited to the matrix phase by the matrix
fraction, ${f_{Mg}}$.

$CR=A+B\times\frac{f_{Mg}}{\sqrt{d}}.$ (13)

Lastly, Bahmani et al. [75] combined the effects of the grain size and
precipitate effects on corrosion into the following model:

$CR=A+B\times\dfrac{f_{Mg}}{\sqrt{D}}+C\times\sum_{i}f_{i}|\Delta E_{i}|.$
(14)

where $f_{i}$ represents the volume fraction of the intermetallic phase
obtained from XRD, and $\Delta E_{i}$ signifies the volta-potential difference
between the intermetallic and Mg matrix. The fit of the Bahmani precipitate
model is listed in Supplementary Figure SI 7.

As per the galvanic series, Mg ranks among the most anodic structural metals,
whereas most secondary phases, with the exception of Mg2Ca, exhibit cathodic
characteristics, rendering Mg more prone to corrosion. [76] The corrosion rate
attributed to micro-galvanic cells due to the presence of intermetallic phases
can be effectively modeled by considering the voltaic potential difference
(obtained from [72]), the kinetics of the reaction, and the volume fraction of
the phase, which represents the available sites for corrosion. The third term
in Equation 14 establishes the correlation between corrosion and the presence
of precipitates. Remarkably, fitting the precipitate model to the corrosion
rate data yields an $R^{2}$ value of 0.87 as shown in Supplementary Figures SI
6 and SI 7.

It has been known that dislocation density and crystallographic texture can
also impact corrosion rates significantly. [75, 38] According to the
literature [77, 75], excess dislocations often accelerate the nucleation and
expansion of pitting and the generation of corrosion products. Texture also
significantly affects the corrosion behavior of Mg alloys as the work function
is different on different crystallographic planes. [34] However, no physical
or numerical models exist to describe their contributions, thus facilitating
the need to correlate them to corrosion rates directly.

To enable this analysis, we first conducted correlation analyses, as shown in
LABEL:subfig:corrosion_pcc, to understand the correlation between
microstructural features and corrosion rate, combining the physical
relationships outlined above. In this data set, we observed positive
correlations for dislocation density and precipitate fraction (with ternary
being the most correlated), consistent with the literature that dislocation
density and precipitates increase the corrosion rates. Additionally,
$(11\overline{2}0/0002)$ texture ratio showed a positive correlation, in line
with literature [38] suggesting that prismatic planes corrode faster, while
$(10\overline{1}0/0002)$ texture ratio exhibited a small negative correlation.
However, this slight negative correlation might be attributed to the
relatively constant intensity of $(10\overline{1}0)$ plane during annealing,
coupled with changes primarily occurring in the $(0002)$ plane. The inverse
square root of grain size also showed a positive correlation, suggesting that
grain size refinement increases corrosion. However, it’s essential to note
that a high correlation does not necessarily equate to influencing corrosion
behavior.

To truly distinguish between these microstructure features and gain insights
into the dominant microstructure, we conducted LASSO fitting, as outlined
below:

$\displaystyle CR$ $\displaystyle=$
$\displaystyle\lambda[A(1/\sqrt{d})+B\rho+C\times\sum_{i}f_{i}|\Delta E|+...$
(15) $\displaystyle...$
$\displaystyle+D\frac{(10\overline{1}0)}{(0002)}+E\frac{(11\overline{2}0)}{(0002)}],$

where A, B, C, D, and E are fitting constants in LASSO that give the feature
importance value. The LASSO regression fit has an accuracy of 81.16%, and the
fit was obtained by optimizing over the $\lambda$ parameter using LOOCV; see
Section 2.5.

The literature presents an interesting and somewhat contradictory perspective
on the relationship between grain size and corrosion rate. Bahmani et al. [72,
34] suggest that an increase in grain size may reduce corrosion rate due to
factors such as decreased lattice strain, dislocation density, and surface
potential. Conversely, a decrease in grain size may lead to a lower corrosion
rate due to the formation of a more uniform and coherent passivation layer,
increased barrier effects at grain boundaries against crystallographic
pitting, and enhancement of basal plane intensity. Despite a positive
correlation observed with $1/\sqrt{d}$ in Pearson R correlation analysis,
LASSO regression (LABEL:subfig:corrosion_lasso) indicates that grain size may
not have a significant impact on corrosion rate for this Mg alloy and under
these processing conditions.

The LASSO analysis, mirroring PCC analyses, reveals that corrosion rates are
predominantly influenced by the ternary Ca2Mg6Zn3 phase. The potential
difference between the intermetallic phase and the matrix drives electrons
from the anode to the cathode, forming galvanic cells. In this electrochemical
process, the anodic second phase degrades upon contact with the nobler matrix
in a galvanic cell, while the matrix degrades when the second phase is nobler
than the matrix. Specifically, Ca2Mg6Zn3 acts as a cathode, and the Mg matrix
serves as an anode at their interface, enabling the formation of a micro
galvanic cell and thereby increasing the corrosion rate. [78, 4, 5]

Mg2Ca exhibits a positive correlation with corrosion and contributes to
corrosion despite being more anodic than Mg [78]. Kim et al. [79] demonstrated
that the formation of a galvanic cell between the Mg anode and Mg2Ca cathode
accelerated the hydrogen evolution rate, thereby increasing corrosion.
However, their impact is relatively minor due to their lower volume fraction
and potential differences compared to the ternary phase.

Despite its positive correlation, the Mn phase appears to play no significant
role in corrosion behavior. While the potential difference [72] indicates that
the Mn phase also acts as a cathode, forming a galvanic couple and leading to
increased corrosion rates as seen in PCC analyses, its extremely low content
in these alloys renders it of minimal impact, as reflected in the LASSO
analysis.

Generally, dislocations act as anodic sites relative to the matrix [75],
leading to a strong positive correlation between dislocation density and
corrosion rate. This effect becomes most pronounced in highly deformed samples
and can even persist following low-temperature thermal treatments in which
dislocations can be fairly stable. For the high-temperature anneals performed
here, the LASSO analysis indicates that dislocation density has little
influence, likely due to the rapid annihilation of dislocations within the
first minute of annealing. Further research incorporating a range of
dislocation densities is necessary to comprehensively grasp their impact on
the corrosion behavior of this Mg alloy.

Similar to dislocations, literature [38] suggests that texture exerts some
influence on corrosion rate. While there is a positive correlation, the LASSO
analysis indicates the impact is negligible for high-temperature thermal
processing of this Mg alloy. The lack of influence can be partly attributed to
the absence of strong texture in this ECAP sample, even following high-
temperature anneals. We argue that a relatively random distribution of
textures effectively nullifies its impact.

##  4 Conclusions

In this study, we used rapid characterization techniques and machine learning
analyses to investigate the complex interplay between thermal processing,
microstructure, hardness, and corrosion rates in an Mg alloy. Utilizing XRD
and optical microscopy, we swiftly characterized microstructural features with
minimal sample preparation, while hardness measurements and 1-day immersion
tests provided rapid insights into mechanical and corrosion behavior,
respectively.

While the anticipated trend of decreasing hardness and corrosion rates with
prolonged high-temperature annealing was observed, intriguing deviations were
noted at short annealing times. Particularly, a 1-minute anneal at
450$\degree$C yielded a favorable combination of high hardness and relatively
low corrosion rate. This brief annealing significantly reduced dislocation
density and dissolved ternary precipitates. Extending the annealing time to
two minutes resulted in a considerable increase in grain size accompanied by
texture variations. These distinct variations underscore the importance of
employing accelerated characterization techniques to capture variations across
various annealing durations.

Despite the challenges posed by strong correlations among microstructural
features and limited data, we successfully established correlations between
microstructural features, hardness, and corrosion rates using machine
learning-based feature selection routes, such as LASSO regression, as well as
Pearson R Correlations in conjunction with physics-based relationships.

Our analysis highlights the significant roles of grain size refinement in
strengthening and the control of corrosion rates by ternary phase fraction, as
revealed by LASSO. Importantly, our findings emphasize that achieving a fine
grain size and reducing the presence of ternary phases and dislocations can
yield an optimal combination of strength and corrosion resistance. These
insights not only enhance our understanding of material behavior but also
offer valuable guidance for processing alloys tailored to specific application
requirements.

##  5 Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal affiliations that might have influenced the findings presented in
this paper.

##  6 Acknowledgements

The authors extend their gratitude to Prof. Todd Hufnagel for insightful
discussions regarding X-ray diffraction analyses, Dr. Karthikeyan Hariharan
for access to the CALPHAD phase diagram, and Mr. Tunde Ayodeji for assisting
with graphical illustrations. Additional thanks to Diana Bershadky, Dr. Suhas
Eswarappa Prameela, Dr. Jenna Krynicki, Mr. Rich Middlestadt, Dr. John Fite,
and Prof. Roger Guillory II for their invaluable insights and support. S.R.
and T.P.W were supported by the National Science Foundation under grant DMR
#2320355. M.S.P. and P.C. were supported by the Department of Energy, Office
of Science, Basic Energy Sciences, under Award #DE-SC0022305 (formulation
engineering of energy materials via multiscale learning spirals). Computing
resources were provided by the ARCH high-performance computing (HPC) facility,
which is supported by National Science Foundation (NSF) grant number OAC
1920103.

## References

  * [1] Frank Witte  “The history of biodegradable magnesium implants: A review”  In _Acta Biomaterialia_ 6.5, 2010, pp. 1680–1692  DOI: 10.1016/j.actbio.2010.02.028
  * [2] Yan Yang et al.  “Research advances in magnesium and magnesium alloys worldwide in 2020”  In _Journal of Magnesium and Alloys_ 9.3, 2021, pp. 705–747  DOI: 10.1016/j.jma.2021.04.001
  * [3] Guangling Song  “Control of biodegradation of biocompatable magnesium alloys”  In _Corrosion Science_ 49.4, 2007, pp. 1696–1701  DOI: 10.1016/j.corsci.2007.01.001
  * [4] J. Hofstetter et al.  “High-Strength Low-Alloy (HSLA) Mg–Zn–Ca Alloys with Excellent Biodegradation Performance”  In _JOM_ 66.4, 2014, pp. 566–572  DOI: 10.1007/s11837-014-0875-5
  * [5] J. Hofstetter et al.  “Processing and microstructure–property relations of high-strength low-alloy (HSLA) Mg–Zn–Ca alloys”  In _Acta Materialia_ 98, 2015, pp. 423–432  DOI: 10.1016/j.actamat.2015.07.021
  * [6] Somasundaram Prasadh, Sreenivas Raguraman, Raymond Wong and Manoj Gupta  “Current Status and Outlook of Temporary Implants (Magnesium/Zinc) in Cardiovascular Applications” Number: 6 Publisher: Multidisciplinary Digital Publishing Institute  In _Metals_ 12.6, 2022, pp. 999  DOI: 10.3390/met12060999
  * [7] Ju Xue et al.  “A biodegradable 3D woven magnesium-based scaffold for orthopedic implants” Publisher: IOP Publishing  In _Biofabrication_ 14.3, 2022, pp. 034107  DOI: 10.1088/1758-5090/ac73b8
  * [8] Somasundaram Prasadh, Sreenivas Raguraman, Raymond Wong and Manoj Gupta  “Metallic Foams in Bone Tissue Engineering”  In _Nanoscale Engineering of Biomaterials: Properties and Applications_ Singapore: Springer Nature, 2022, pp. 181–205  DOI: 10.1007/978-981-16-3667-7˙7
  * [9] Sean Whooley  “FDA approves bioresorbable metal implant from Bioretec”  In _MassDevice_ , 2023  URL: https://www.massdevice.com/fda-approves-bioresorbable-metal-implant-bioretec/
  * [10] Qin Wu et al.  “Dynamic Precipitation, Dynamic Recrystallization, and Texture Evolution of Mg–5Zn Alloy Sheets with Trace Ca and Sr Additions” Publisher: Cambridge University Press  In _Microscopy and Microanalysis_ 26.5, 2020, pp. 886–894  DOI: 10.1017/S1431927620024356
  * [11] J.. Bhattacharyya, B. Radhakrishnan, G. Muralidharan and S.. Agnew  “Texture Evolution During Grain Growth of Magnesium Alloy AZ31B”  In _Magnesium Technology 2014_ Cham: Springer International Publishing, 2016, pp. 233–238  DOI: 10.1007/978-3-319-48231-6˙45
  * [12] F.. Humphreys and M.. Ardakani  “Grain boundary migration and Zener pinning in particle-containing copper crystals”  In _Acta Materialia_ 44.7, 1996, pp. 2717–2727  DOI: 10.1016/1359-6454(95)00421-1
  * [13] David Freedman, Robert Pisani and Roger Purves  “Statistics (international student edition)”  In _Pisani, R. Purves, 4th edn. WW Norton & Company, New York_, 2007
  * [14] Robert Tibshirani  “Regression Shrinkage and Selection via the Lasso”  In _Journal of the Royal Statistical Society. Series B (Methodological)_ 58.1, 1996, pp. 267–288  URL: https://www.jstor.org/stable/2346178
  * [15] Atwakyire Moses, Ding Chen, Peng Wan and Siyuan Wang  “Prediction of electrochemical corrosion behavior of magnesium alloy using machine learning methods”  In _Materials Today Communications_ 37, 2023, pp. 107285  DOI: 10.1016/j.mtcomm.2023.107285
  * [16] Joung Sik Suh, Byeong-Chan Suh, Jun Ho Bae and Young Min Kim  “Machine learning-based design of biodegradable Mg alloys for load-bearing implants”  In _Materials & Design_ 225, 2023, pp. 111442  DOI: 10.1016/j.matdes.2022.111442
  * [17] Parham Valipoorsalimi, Yuksel Asli Sari and Mihriban Pekguleryuz  “Mechanical Property Design of Bio-compatible Mg alloys using Machine-Learning Algorithms” arXiv:2305.12060 [cond-mat]  arXiv, 2023  DOI: 10.48550/arXiv.2305.12060
  * [18] Casey F. Davis, Adam J. Griebel and Terry C. Lowe  “Isothermal Continuous Equal Channel Angular Pressing of Magnesium Alloy AZ31”  In _JOM_ 72.7, 2020, pp. 2603–2611  DOI: 10.1007/s11837-020-04195-4
  * [19] E04 Committee  “Practice for Microetching Metals and Alloys”  ASTM International  DOI: 10.1520/E0407-07R15E01
  * [20] E04 Committee  “Test Methods for Determining Average Grain Size”  ASTM International  DOI: 10.1520/E0112-13R21
  * [21] J. Wheeler et al.  “The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials”  In _Journal of Microscopy_ 233.3, 2009, pp. 482–494  DOI: 10.1111/j.1365-2818.2009.03136.x
  * [22] Nobuyuki Otsu  “A Threshold Selection Method from Gray-Level Histograms” Conference Name: IEEE Transactions on Systems, Man, and Cybernetics  In _IEEE Transactions on Systems, Man, and Cybernetics_ 9.1, 1979, pp. 62–66  DOI: 10.1109/TSMC.1979.4310076
  * [23] Bernard Dennis Cullity  “Elements of X-ray Diffraction”  Addison-Wesley Publishing, 1956  URL: http://117.239.25.194:7000/jspui/bitstream/123456789/954/1/PRELIMINARY%20AND%20CONTENT.pdf
  * [24] G. Ribárik, T. Ungár and J. Gubicza  “MWP-fit: a program for multiple whole-profile fitting of diffraction peak profiles by ab initio theoretical functions” Publisher: International Union of Crystallography  In _Journal of Applied Crystallography_ 34.5, 2001, pp. 669–676  DOI: 10.1107/S0021889801011451
  * [25] G. Ribárik, J. Gubicza and T. Ungár  “Correlation between strength and microstructure of ball-milled Al–Mg alloys determined by X-ray diffraction”  In _Materials Science and Engineering: A_ 387-389, 13th International Conference on the Strength of Materials, 2004, pp. 343–347  DOI: 10.1016/j.msea.2004.01.089
  * [26] Gyan Shankar, Sreenivas Raguraman, Luis A. Barrales-Mora and S. Suwas  “Development of Recrystallization Texture in Commercially Pure Titanium: Experiments and Simulation”  In _JOM_ 72.12, 2020, pp. 4559–4573  DOI: 10.1007/s11837-020-04447-3
  * [27] S.. Agnew et al.  “X-ray diffraction line profile analysis for the detection of the propensity to sensitize”  In _Materials Science and Engineering: A_ 871, 2023, pp. 144900  DOI: 10.1016/j.msea.2023.144900
  * [28] Scott A. Speakman  “Profile Fitting for Analysis of XRPD Data using HighScore Plus v3”  In _Massachusetts Institute of Technology, Cambridge MA_ , 2012  URL: http://prism.mit.edu/XRAY/4%20Profile%20Fitting%20for%20Quantitative%20Analysis.pdf
  * [29] Shima Ehtemam-Haghighi, Yujing Liu, Guanghui Cao and Lai-Chang Zhang  “Phase transition, microstructural evolution and mechanical properties of Ti-Nb-Fe alloys induced by Fe addition”  In _Materials & Design_ 97, 2016, pp. 279–286  DOI: 10.1016/j.matdes.2016.02.094
  * [30] “DIN EN ISO 6507-1:2018-07, Metallische Werkstoffe_- Härteprüfung nach Vickers_- Teil_1: Prüfverfahren (ISO_6507-1:2018); Deutsche Fassung EN_ISO_6507-1:2018”  Beuth Verlag GmbH  DOI: 10.31030/2778746
  * [31] J01 Committee  “Guide for Laboratory Immersion Corrosion Testing of Metals”  DOI: 10.1520/G0031-72R04
  * [32] G01 Committee  “Practice for Preparing, Cleaning, and Evaluating Corrosion Test Specimens”  ASTM International  DOI: 10.1520/G0001-03R17E01
  * [33] Sreenivas Raguraman et al.  “Impact of Thermo-Mechanical Processing on Structure–Property Relationships for the Biodegradable ZX10 Mg Alloy”  In _Magnesium Technology 2024_ , The Minerals, Metals & Materials Series  Cham: Springer Nature Switzerland, 2024, pp. 213–216  DOI: 10.1007/978-3-031-50240-8˙40
  * [34] Ahmad Bahmani, Mehrab Lotfpour, Milad Taghizadeh and Woo-Jin Kim  “Corrosion behavior of severely plastically deformed Mg and Mg alloys”  In _Journal of Magnesium and Alloys_ 10.10, 2022, pp. 2607–2648  DOI: 10.1016/j.jma.2022.09.007
  * [35] Garima Kapoor et al.  “The Influence of Severe Plastic Deformation and Subsequent Annealing on the Microstructure and Hardness of a Cu–Cr–Zr Alloy”  In _Materials_ 13.10, 2020, pp. 2241  DOI: 10.3390/ma13102241
  * [36] Mária Zemková et al.  “Influence of heat treatment on corrosion resistance of Mg-Al-Zn alloy processed by severe plastic deformation”  In _Open Engineering_ 8.1, 2018, pp. 391–394  DOI: 10.1515/eng-2018-0044
  * [37] Shangshu Wu et al.  “Dislocation exhaustion and ultra-hardening of nanograined metals by phase transformation at grain boundaries”  In _Nature Communications_ 13.1, 2022, pp. 5468  DOI: 10.1038/s41467-022-33257-1
  * [38] Ehsan Gerashi, Reza Alizadeh and Terence G. Langdon  “Effect of crystallographic texture and twinning on the corrosion behavior of Mg alloys: A review”  In _Journal of Magnesium and Alloys_ 10.2, 2022, pp. 313–325  DOI: 10.1016/j.jma.2021.09.009
  * [39] Wei Zhong and Ji-Cheng Zhao  “A comprehensive diffusion mobility database comprising 23 elements for magnesium alloys”  In _Acta Materialia_ 201, 2020, pp. 191–208  DOI: 10.1016/j.actamat.2020.09.079
  * [40] Jian-Feng Nie  “Precipitation and Hardening in Magnesium Alloys”  In _Metallurgical and Materials Transactions A_ 43.11, 2012, pp. 3891–3939  DOI: 10.1007/s11661-012-1217-2
  * [41] Xukai Zhang, M.-X Guo, Jishan Zhang and Linzhong Zhuang  “Dissolution of Precipitates During Solution Treatment of Al-Mg-Si-Cu Alloys”  In _Metallurgical and Materials Transactions B_ 47, 2015  DOI: 10.1007/s11663-015-0500-1
  * [42] Meysam Mohammadi Zerankeshi et al.  “Effects of heat treatment on the corrosion behavior and mechanical properties of biodegradable Mg alloys”  In _Journal of Magnesium and Alloys_ 10.7, 2022, pp. 1737–1785  DOI: 10.1016/j.jma.2022.04.010
  * [43] Shuai Liu and Hanjie Guo  “Influence of Heat Treatment on Microstructure and Mechanical Properties of AZ61 Magnesium Alloy Prepared by Selective Laser Melting (SLM)”  In _Materials_ 15.20, 2022, pp. 7067  DOI: 10.3390/ma15207067
  * [44] Yang He et al.  “Quantitative study of dissolution of Mg2Si during solution treatment in AA6014 alloy”  In _Journal of Alloys and Compounds_ 703, 2017, pp. 272–279  DOI: 10.1016/j.jallcom.2017.01.336
  * [45] Qinghua Chen et al.  “The mechanisms of grain growth of Mg alloys: A review”  In _Journal of Magnesium and Alloys_ 10.9, 2022, pp. 2384–2397  DOI: 10.1016/j.jma.2022.09.001
  * [46] D. Panda et al.  “Texture weakening in pure magnesium during grain growth”  In _Philosophical Magazine_ 99.11, 2019, pp. 1362–1385  DOI: 10.1080/14786435.2019.1581382
  * [47] J.. Burke and D. Turnbull  “Recrystallization and grain growth”  In _Progress in Metal Physics_ 3, 1952, pp. 220–292  DOI: 10.1016/0502-8205(52)90009-9
  * [48] J.. Bhattacharyya, S.. Agnew and G. Muralidharan  “Texture enhancement during grain growth of magnesium alloy AZ31B”  In _Acta Materialia_ 86, 2015, pp. 80–94  DOI: 10.1016/j.actamat.2014.12.009
  * [49] Risheng Pei, Sandra Korte-Kerzel and Talal Al-Samman  “Normal and abnormal grain growth in magnesium: Experimental observations and simulations”  In _Journal of Materials Science & Technology_ 50, 2020, pp. 257–270  DOI: 10.1016/j.jmst.2020.01.014
  * [50] A.. Rollett, D.. Srolovitz and M.. Anderson  “Simulation and theory of abnormal grain growth—anisotropic grain boundary energies and mobilities”  In _Acta Metallurgica_ 37.4, 1989, pp. 1227–1240  DOI: 10.1016/0001-6160(89)90117-X
  * [51] D. Srolovitz, G. Grest and M. Anderson  “Computer simulation of grain growth—V. Abnormal grain growth”  In _Acta Metallurgica_ 33.12, 1985, pp. 2233–2247  DOI: 10.1016/0001-6160(85)90185-3
  * [52] JoséCarlos Bruno and Paulo Rangel Rios  “The grain size distribution and the detection of abnormal grain growth of austenite in an eutectoid steel containing niobium”  In _Scripta Metallurgica et Materialia_ 32.4, 1995, pp. 601–606  DOI: 10.1016/0956-716X(95)90844-A
  * [53] P.. Manohar, M. Ferry and T. Chandra  “Five Decades of the Zener Equation”  In _ISIJ International_ 38.9, 1998, pp. 913–924  DOI: 10.2355/isijinternational.38.913
  * [54] Suhas Eswarappa Prameela et al.  “Strengthening magnesium by design: Integrating alloying and dynamic processing”  In _Mechanics of Materials_ 167, 2022, pp. 104203  DOI: 10.1016/j.mechmat.2021.104203
  * [55] Isaac Toda-Caraballo, Enrique I. Galindo-Nava and Pedro E.. Rivera-Díaz-del-Castillo  “Understanding the factors influencing yield strength on Mg alloys”  In _Acta Materialia_ 75, 2014, pp. 287–296  DOI: 10.1016/j.actamat.2014.04.064
  * [56] Jun Wang et al.  “Multi-solute solid solution behavior and its effect on the properties of magnesium alloys”  In _Journal of Magnesium and Alloys_ 10.7, 2022, pp. 1786–1820  DOI: 10.1016/j.jma.2022.06.015
  * [57] Z.. Cordero, B.. Knight and C.. Schuh  “Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals”  In _International Materials Reviews_ 61.8, 2016, pp. 495–512  DOI: 10.1080/09506608.2016.1191808
  * [58] Chuangye Wang, Wei Zhong, Jess Garnett and Ji-Cheng Zhao  “High-Throughput Evaluation of Hardening Coefficients of Eight Alloying Elements in Magnesium”  In _Advanced Engineering Materials_ n/a, pp. 2300847  DOI: 10.1002/adem.202300847
  * [59] Partha Duley, Souriddha Sanyal, T.. Bandyopadhyay and Sumantra Mandal  “Implications of annealing treatments on microstructure, texture, and tensile properties of hard plate hot forged Mg-Zn-Ca-Mn alloy”  In _Materials Characterization_ 172, 2021, pp. 110885  DOI: 10.1016/j.matchar.2021.110885
  * [60] Suhas Eswarappa Prameela et al.  “Rapid Quantification of Dynamic and Spall Strength of Metals Across Strain Rates” arXiv:2309.14296 [cond-mat]  arXiv, 2023  URL: http://arxiv.org/abs/2309.14296
  * [61] Partha Duley, Souriddha Sanyal, T.. Bandyopadhyay and Sumantra Mandal  “Implications of grain size distribution, precipitate evolution and texture development on tensile properties in hard plate hot forged and annealed Mg–Zn–Ca–Mn alloy”  In _Materials Science and Engineering: A_ 784, 2020, pp. 139288  DOI: 10.1016/j.msea.2020.139288
  * [62] Uwe Holzwarth and Neil Gibson  “The Scherrer equation versus the ’Debye-Scherrer equation”’ Number: 9 Publisher: Nature Publishing Group  In _Nature Nanotechnology_ 6.9, 2011, pp. 534–534  DOI: 10.1038/nnano.2011.145
  * [63] J.. Nie  “Effects of precipitate shape and orientation on dispersion strengthening in magnesium alloys”  In _Scripta Materialia_ 48.8, ViewPoint Set No. 29 ”Phase Transformations and Deformations in Magnesium Alloys”, 2003, pp. 1009–1015  DOI: 10.1016/S1359-6462(02)00497-9
  * [64] P. Zhang, S.. Li and Z.. Zhang  “General relationship between strength and hardness”  In _Materials Science and Engineering: A_ 529, 2011, pp. 62–73  DOI: 10.1016/j.msea.2011.08.061
  * [65] G Nussbaum, P Sainfort, G Regazzoni and H Gjestland  “Strengthening mechanisms in the rapidly solidified AZ 91 magnesium alloy”  In _Scripta Metallurgica_ 23.7 Elsevier, 1989, pp. 1079–1084
  * [66] Jinhua Peng et al.  “The effect of texture and grain size on improving the mechanical properties of Mg-Al-Zn alloys by friction stir processing”  In _Scientific Reports_ 8.1 Nature Publishing Group UK London, 2018, pp. 4196
  * [67] Sen Wang et al.  “Grain refinement and strength enhancement in Mg wrought alloys: A review”  In _Journal of Magnesium and Alloys_ , 2023  DOI: 10.1016/j.jma.2023.11.002
  * [68] CY Wang, Carmen Maria Cepeda-Jimenez and Maria Teresa Pérez-Prado  “Dislocation-particle interactions in magnesium alloys”  In _Acta Materialia_ 194 Elsevier, 2020, pp. 190–206
  * [69] Feilong Guo et al.  “The mechanism for the different effects of texture on yield strength and hardness of Mg alloys” Number: 1 Publisher: Nature Publishing Group  In _Scientific Reports_ 7.1, 2017, pp. 8647  DOI: 10.1038/s41598-017-08966-z
  * [70] Joost J Vlassak and WD Nix  “Measuring the elastic properties of anisotropic materials by means of indentation experiments”  In _Journal of the Mechanics and Physics of Solids_ 42.8 Elsevier, 1994, pp. 1223–1245
  * [71] K.. Ralston, N. Birbilis and C… Davies  “Revealing the relationship between grain size and corrosion rate of metals”  In _Scripta Materialia_ 63.12, 2010, pp. 1201–1204  DOI: 10.1016/j.scriptamat.2010.08.035
  * [72] Ahmad Bahmani, Srinivasan Arthanari and Kwang Seon Shin  “Corrosion behavior of Mg–Mn–Ca alloy: Influences of Al, Sn and Zn”  In _Journal of Magnesium and Alloys_ 7.1, 2019, pp. 38–46  DOI: 10.1016/j.jma.2018.11.004
  * [73] Jihua Chen et al.  “Correlation between microstructure and corrosion resistance of magnesium alloys prepared by high strain rate rolling”  In _Journal of Materials Engineering and Performance_ 26 Springer, 2017, pp. 4748–4759
  * [74] Dan Song et al.  “Corrosion behaviour of bulk ultra-fine grained AZ91D magnesium alloy fabricated by equal-channel angular pressing”  In _corrosion science_ 53.1 Elsevier, 2011, pp. 362–373
  * [75] Ahmad Bahmani, Srinivasan Arthanari and Kwang Seon Shin  “Formulation of corrosion rate of magnesium alloys using microstructural parameters”  In _Journal of Magnesium and Alloys_ 8.1, 2020, pp. 134–149  DOI: 10.1016/j.jma.2019.12.001
  * [76] A.. Südholz, N.. Kirkland, R.. Buchheit and N. Birbilis  “Electrochemical Properties of Intermetallic Phases and Common Impurity Elements in Magnesium Alloys”  In _Electrochemical and Solid-State Letters_ 14.2, 2010, pp. C5  DOI: 10.1149/1.3523229
  * [77] Jiahao Jiang, Xue Geng and Xiaobo Zhang  “Stress corrosion cracking of magnesium alloys: A review”  In _Journal of Magnesium and Alloys_ 11.6, 2023, pp. 1906–1930  DOI: 10.1016/j.jma.2023.05.011
  * [78] Erlin Zhang and Lei Yang  “Microstructure, mechanical properties and bio-corrosion properties of Mg–Zn–Mn–Ca alloy for biomedical application”  In _Materials Science and Engineering: A_ 497.1-2 Elsevier, 2008, pp. 111–118
  * [79] Woo-Cheol Kim, Jung-Gu Kim, Ji-Young Lee and Hyun-Kwang Seok  “Influence of Ca on the corrosion properties of magnesium for biomaterials”  In _Materials Letters_ 62.25 Elsevier, 2008, pp. 4146–4148

##  Appendix A Supplementary Information

### A.1 Grain Size Measurements

Condition Time (hr) Mean ($\mathbf{\mu}$m) St.Dev Minimum ($\mathbf{\mu}$m)
Maximum $\mathbf{\mu}$m) ECAP 0 0.83 0.35 0.33 2.11 1 min 0.02 0.84 0.40 0.24
2.29 2 min 0.07 11.52 4.73 2.32 20.78 5 min 0.08 19.39 9.97 3.14 51.34 15 min
0.25 18.17 12.76 3.29 66.01 30 min 0.50 20.82 12.87 2.10 62.42 1 hr 1.00 21.27
12.37 4.89 62.20 4 hr 4.00 25.66 12.89 4.46 58.86 16 hr 16.00 27.61 17.88 6.34
99.99 64 hr 64.00 40.39 29.04 5.41 158.34 128 hr 128.00 49.40 23.42 11.03
137.49

Table SI 1: Grain Size Statistics

### A.2 Normalized Grain Size Distributions

Figure SI 0: Normalized Grain Size Distributions

### A.3 Goodness of Log-normal fit

We can see log-normal distributions throughout, except in the 2-minute
scenario where $\chi^{2}<0.05$.

Condition | Time | Breadth | $\mathbf{\chi^{2}}$
---|---|---|---
ECAP | 0.00 | 1.85 | 0.12
1 min | 0.02 | 2.26 | 0.89
2 min | 0.03 | 2.19 | 0.02
5 min | 0.08 | 2.53 | 0.21
15 min | 0.25 | 3.10 | 0.48
30 min | 0.50 | 3.39 | 0.19
1 hr | 1.00 | 2.54 | 0.66
4 hr | 4.00 | 2.58 | 0.26
16 hr | 16.00 | 2.76 | 0.88
64 hr | 64.00 | 3.38 | 0.83
128 hr | 128.00 | 2.52 | 0.53
Table SI 2: Log-normal grain size distribution

### A.4 Geometrically Necessary Dislocation Maps

The GND maps obtained from EBSD revealing

Figure SI 1: GND Distribution Maps

### A.5 Precipitate Size and Spacing

Condition | Mean Precipitate Diameter (nm) | Mean Particle Spacing (nm)
---|---|---
Ca2Mg6Zn3 |  Mg2Ca |  Mn |  Ca2Mg6Zn3 |  Mg2Ca |  Mn
ECAP | 149.30 | 117.58 | 131.00 | 277.77 | 374.66 | 473.76
1 min | 147.81 | 129.50 | 148.07 | 345.53 | 432.92 | 663.54
2 min | 158.73 | 116.73 | 214.17 | 385.68 | 395.52 | 965.69
5 min | 146.14 | 146.83 | 161.08 | 357.84 | 486.68 | 746.53
15 min | 151.20 | 109.10 | 104.77 | 373.95 | 368.60 | 462.26
30 min | 150.91 | 194.96 | 168.10 | 373.59 | 651.65 | 759.71
1 hr | 137.44 | 132.64 | 153.98 | 293.44 | 363.97 | 518.52
4 hr | 157.93 | 136.20 | 114.55 | 343.34 | 395.16 | 382.39
16 hr | 131.87 | 180.60 | 171.67 | 298.72 | 531.36 | 606.25
64 hr | 126.42 | 129.02 | 168.75 | 335.67 | 386.09 | 677.80
128 hr | 175.17 | 172.12 | 130.17 | 501.92 | 647.61 | 523.19

Table SI 3: Precipitate Size and Spacing estimated through XRD

### A.6 Strengthening Mechanism Models

####  A.6.1 Hall Petch Model

The Hall Petch model ($H_{V}=kd^{-0.5}$) exhibited a superior fit of 89.4%,
denoting a dominant influence of grain boundaries on strengthening.

Figure SI 2: Hall Petch Strengthening

####  A.6.2 Taylor Dislocation Model

The poor fit ($R^{2}=0.45$) of the Taylor dislocation model
($\sigma_{dis}=M\alpha Gb\sqrt{\rho}$) represents the suppressed roles of
dislocation density in strengthening this material.

Figure SI 3: Dislocation Strengthening

####  A.6.3 Orowan Strengthening Model

The poor fits of the Orowan model upon strengthening from the ternary
($R^{2}=0.625$), binary ($R^{2}=0.4715$), and Mn ($R^{2}=0.34$) denote the
limited roles of precipitates in strengthening this material.

### A.7 Corrosion Mechanism Models

####  A.7.1 Ralston-Birbilis Model

We fitted our grain sizes to corrosion using the Ralston-Birbilis model
elaborated in Equation 12. We found a poor fit of 46%, denoting the suppressed
role of grain size in corrosion behavior.

Figure SI 6: Ralston-Bibilis Grain Size Model - as a function of solution heat
treatment

####  A.7.2 Bahmani Model

We fitted our precipitate contributions to corrosion using the Bahmani
precipitate model, as shown below:

$CR=A+C\times[f_{\text{Ca}_{2}\text{Mg}_{6}\text{Zn}_{3}}|\Delta
E_{\text{Ca}_{2}\text{Mg}_{6}\text{Zn}_{3}}|+f_{\text{Mg}_{2}\text{Ca}}|\Delta
E_{\text{Mg}_{2}\text{Ca}}|+f_{\text{Mn}}|\Delta E_{\text{Mn}}|]$ (16)

We observed a superior fit of 88%, denoting the dominance of the precipitates
on the corrosion behavior.

Figure SI 7: Bahmani Precipitate Model - as a function of solution heat
treatment