# The dynamic evolution of swelling in nickel concentrated solid solution
alloys through _in situ_ property monitoring

Cody A. Dennett<EMAIL_ADDRESS>Materials Science and Engineering
Department, Idaho National Laboratory, Idaho Falls, ID 83415, USA  Department
of Nuclear Science and Engineering, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Benjamin R. Dacus  Department of Nuclear Science and
Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Christopher M. Barr  Center for Integrated Nanotechnologies, Sandia National
Laboratories, Albuquerque, NM 87185, USA  Trevor Clark  Center for Integrated
Nanotechnologies, Sandia National Laboratories, Albuquerque, NM 87185, USA
Hongbin Bei  Materials Science and Technology Division, Oak Ridge National
Laboratory, Oak Ridge, TN 73830, USA  Yanwen Zhang  Materials Science and
Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 73830, USA
Michael P. Short  Department of Nuclear Science and Engineering, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  Khalid Hattar  Center for
Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM
87185, USA

###### Abstract

While the high-temperature void swelling behavior in Ni-based concentrated
solid solution alloys (CSAs) has received much attention, work to date has
relied on traditional, post-irradiation microscopy to quantify swelling. Here,
the dynamic evolution of swelling in five alloys of increasing complexity is
observed using continuous, _in situ_ measurements of thermoelastic properties
in bulk specimens under ion beam irradiation. The evolution in elastic
properties during swelling is found to be a function of the entire size
spectrum of defects, not solely the mesoscale voids observed using microscopy,
while changes in thermal transport properties depend sensitively on the
partitioning of electronic and lattice thermal conductivity. This emerging
class of _in situ_ experiments provides unique insight into material dynamics
otherwise unavailable using traditional methods.

concentrated solid solution alloys, _in situ_ irradiation, swelling,
thermophysical properties

##  I Introduction

Complex concentrated solid solution alloys (CSAs) – often classed as medium or
high entropy alloys depending on their number of alloying elements – host
unique intrinsic properties including local lattice distortions and sluggish
heterogeneous diffusion which have prompted their study as radiation-tolerant
structural materials for advanced energy applications Zhang  _et al._ (2015,
2019). A growing body of experimental and computational work dedicated to
nanoscale defect diffusion Kottke  _et al._ (2019); Zhao  _et al._ (2017),
chemical segregation Tuomisto  _et al._ (2020); Cao (2021), and mesocale
microstructure evolution Zhang  _et al._ (2019); Fan  _et al._ (2021) has been
produced using nickel-based, single phase CSAs as a model system. Several
research efforts have focused specifically on the high-damage suppression of
void swelling in Ni-CSAs using ion beam irradiation and have observed a
general trend of decreased swelling with increasing chemical complexity
attributed to both sluggish diffusion and preferential segregation around
voids and vacancy clusters Lu  _et al._ (2016); n. Yang  _et al._ (2017); Fan
_et al._ (2020). These studies also routinely note a unique effect of
significant void swelling beneath the surface ion damaged layer, in contrast
to pure metallic systems. Prior efforts focused on temperatures in the range
of 400–700∘C, where void swelling is expected to be strongest Boothby (2012)
and have found the greatest degree of swelling to occur at about half the
melting temperature in keeping with well-known trends for pure metals and
traditional alloys Fan  _et al._ (2020).

While noting that the long timescale dynamical behavior of damage accumulation
and swelling are of particular interest in this family of alloys, experimental
studies to date have largely made use of traditional post-irradiation
examination tools (electron microscopy, ion beam analysis, etc.) to capture
snapshots of microstructure and properties at coarse temporal fidelity
following exposure. This restriction has been driven by a combination of
unique constraints involved in the investigation of irradiation-induced
swelling. Significant volumetric swelling is a bulk material effect, rendering
the thin, electron transparent films used in _in situ_ irradiation microscopy
experiments unsuitable despite success shown in observing the earliest stages
of void nucleation Xu  _et al._ (2013). The few available bulk, or bulk-like,
_in situ_ irradiation metrology techniques available, Raman spectroscopy Miro
_et al._ (2016) or piezo-ultrasonic devices Sha  _et al._ (2020), are largely
unsuited to structural metallic samples. Recently, however, new capabilities
combining laser photoacoustics with high temperature ion beam irradiation have
become available which are perfectly suited to the study of the dynamic
temporal evolution of swelling in Ni-CSAs Dennett  _et al._ (2019, 2020).

In this work, high-temperature ion beam irradiation is conducted with
continuous thermoelastic property monitoring to observe the dynamic swelling
response of Ni-CSAs in real-time. Single crystals of Ni and equiatomic NiFe,
NiCoCr, and NiFeCoCr, as well as large-grained polycrystalline NiFeCoCrMn, are
exposed to 31 MeV Ni self-ion irradiation at 550∘C to 60 displacements per
atom (dpa) at the damage peak with _in situ_ property monitoring. These ion
beam energies are chosen to ensure that the thickness of the imposed damage
layer matches the penetration depth of the surface acoustic wave (SAW) induced
to monitor the real-time elastic properties. Dynamic records show elastic
property evolution characteristic of face centered cubic (FCC) metals
undergoing radiation-induced void swelling Dennett  _et al._ (2019, 2020,
2018), with notable variations between alloy chemistries. Post-exposure
scanning transmission electron microscopy (STEM) confirms depth dependent
swelling profiles similar to those observed previously in this family of
alloys. Compared with post-exposure STEM, features of the dynamic elastic
profiles indicate that nanoscale microstructural features down to the level of
mono-vacancies play a significant role in the measured properties,
particularly in the case of ternary NiCoCr.

##  II Materials and methods

A single crystal nickel sample with {001} surface orientation, $\pm 2^{\circ}$
misorientation, and $>$99.99% purity was purchased from the MTI Corporation as
the reference material for this study. For Ni-CSAs, ingots were prepared by
arc-melting an equiatomic proportion of elemental Ni, Co, Fe, Cr, and Mn
($>$99.9% purity), re-melting multiple times to ensure homogenity, and drop
casting into copper molds. Single crystals of NiFe, NiCoCr, and NiFeCoCr were
refined from arc-melted ingots through directional solidification Bei and
George (2005). A refining procedure for quinary alloy was not available at the
time of sample synthesis. All samples were mechanically polished to a mirror
finish. Prior to _in situ_ irradiation, the three single crystal Ni-CSA
samples were measured on a benchtop transient grating spectroscopy (TGS)
experiment described previously by Dennett and Short Dennett and Short (2017).
Briefly, TGS is a pump-probe photoacoustic technique which can be used to
simultaneously capture the propagation speed of surface acoustic waves (SAWs)
of various characters depending on crystal anisotropy and surface layering as
well as surface thermal diffusivity Hofmann  _et al._ (2019); Dennett and
Short (2018). The excitation takes the form of a one dimensional pulsed laser
intensity profile projected onto the sample surface, generated by crossing two
532 nm laser pulses at a fixed angle with $\sim$300 ps duration, with energy
of $\sim$1 µJ, and repetition rate of 1 kHz Maznev  _et al._ (1998). The angle
of beam crossing is selectable by the optical geometry and allows the fringe
(or ‘grating’) spacing to be selected within a range of approximately
$\Lambda=1-10$ µm. Initial characterization is carried out using a grating
spacing of 4.82 µm as determined using a single-crystal tungsten calibration
standard Dennett and Short (2017, 2018). The resulting thermoelastic
excitation is monitored through the use of a 785 nm continuous wave (CW) probe
laser by diffraction from both the physical displacement associated with the
induced SAW as well as any temperature-dependent changes in refractive index,
amplified through the use of a heterodyne detection scheme Maznev  _et al._
(1998); Dennett and Short (2018).

As anisotropic single crystals, the SAW velocity on {001} crystal faces varies
as a function of angular polarization Every  _et al._ (2013), with a minimum
expected for a SAW along $\langle 100\rangle${001} directions. SAW velocity
maps on NiFe, NiCoCr, and NiFeCoCr single crystals were measured in 5∘
increments using a manual sample rotation stage to roughly identify a $\langle
100\rangle$ surface direction prior to ion irradiation experiments. fig. 1(a)
shows measured orientation-dependent SAW velocities for NiFe, NiCoCr, and
NiFeCoCr as well as SAW velocities for pure Ni computed using an elastodynamic
Green’s function method Every  _et al._ (2013); Du and Zhao (2017) using
literature values for the room-temperature elastic constants Epstein and
Carlson (1965). A sharp jump in the measured SAW velocity at approximately
20-25∘ from the $\langle 100\rangle$ indicates the transition of the dominant
acoustic mode from a purely surface-confined Rayleigh-type mode, to a pseudo-
surface mode which penetrates further into the bulk of the crystal Every  _et
al._ (2013). For _in situ_ ion irradiation experiments, the surface acoustic
wave must be confined to as shallow a depth as possible to restrict the
elastic propagation to the ion-modified surface layer. As such, following
benchtop measurement, a $\langle 100\rangle${001} direction on each single
crystal was marked using a diamond scribe to ease the rough alignment of
crystals prior to _in situ_ measurement.

Figure 1: (a) SAW velocity as a function of surface polarization on available
Ni CSA {001} single crystals. Values for pure Ni are calculated using
literature values for elastic constants and alloy samples are experimentally
measured. (b) Normalized depth distribution of displacement damage induced by
31 MeV Ni5+ ions in pure Ni at 550∘C as well as vertical SAW displacement
along $\langle$100$\rangle${001} showing the overlap of the damaged and
excited regions. The dashed vertical line indicates the applied _in situ_
transient grating wavelength of 4.54 µm. The color map above indicates the
relative level of displacement damage and is used in fig. 3.

_In situ_ irradiations were conducted using the _in situ_ ion irradiation TGS
beamline, described in detail elsewhere Dennett  _et al._ (2019). This
facility consists of a free-space TGS optical geometry launched into one end
station of the 6 MV EN Tandem Van de Graaff-Pelletron accelerator located at
Sandia National Laboratories. The minimum available transient grating spacing
in this experiment is $\sim$4.5 µm due to optical access constraints Dennett
_et al._ (2019). An irradiation temperature of 550∘C was selected based on the
range of temperatures for which swelling has been observed in Ni-CSA systems
n. Yang  _et al._ (2019); Fan  _et al._ (2020). As such, a series of
simulations were carried out using the Stopping Range of Ions in Matter (SRIM)
code to determine that 31 MeV Ni ions best match the penetration depth of the
induced acoustic wave. SRIM simulations are conducted for each alloy
compositions using densities inferred from measurements of the lattice
parameter at 550∘C Jin  _et al._ (2017) in the quick Kinchin-Pease (KP) mode
using a uniform displacement energy of 40 eV for each element Ziegler  _et
al._ (2010); Stoller  _et al._ (2013), accounting for the 9.5∘ incidence angle
of the ion beam for I3TGS targets Dennett  _et al._ (2019). While recent work
has shown full-cascade TRIM simulations are better able to capture the total
displacement damage in multicomponent systems Weber and Zhang (2019), doses
inferred from quick KP damage calculations will be referenced throughout this
work to compare most directly with previous work in these systems Lu  _et al._
(2016); n. Yang  _et al._ (2017); Fan  _et al._ (2020). fig. 1(b) shows a
normalized representative SRIM-calculated damage profile for 31 MeV Ni5+ ions
in pure Ni at 550∘C overlaid on the vertical displacement profile calculated
for a Rayleigh-type SAW at this polarization Royer and Dieulesaint (1984).
Although only the profile for pure Ni is shown here, simulations carried out
for each alloy composition are used in determining the applied damage in dpa.
Calculated damage profiles from both quick KP and full cascade simulations are
shown for each alloy composition in Supplementary Fig. S1. Nodes in the SAW
displacement magnitude indicate that portions of the surface displacement
oscillate out-of-phase with one another as a function of depth from the
surface. As shown, by strategically choosing the ion beam energy, the SAW will
be localized to the damaged surface region, returning an elastic response
representative of an average of the heterogeneously-damaged surface layer. The
induced thermal wave penetration scales with $\Lambda/\pi$, indicating that
for damaged microstructures the measured thermal properties will be
representative of a smaller, nearer-surface volume as compared to the acoustic
response Hofmann  _et al._ (2015a); Dennett  _et al._ (2019).

Prior to _in situ_ ion beam exposure, a surface fiducial in the form of a 1 mm
square was scribed into the center of each sample to be used for laser
targeting. Prior to installation, each sample was cleaned with alcohol and
subject to a 15 minute low-energy plasma cleaning to minimize any surface
contamination. Once roughly aligned from benchtop polarization markings,
samples were azimuthally rocked through $\sim$10∘ while the frequency of the
induced SAW is monitored to ensure that they are aligned along the minimum SAW
velocity direction corresponding to a $\langle 100\rangle${001} surface
polarization. For _in situ_ TGS measurements, the excitation laser spot was
$\sim$200 µm in diameter and the probing laser spot was $\sim$100 µm in
diameter. _In situ_ TGS measurements were collected using a 30 second time
domain average of the 1 kHz repetition rate to increase the collected signal-
to-noise ratio. In practice, measurements are collected on a 50% duty cycle to
allow for any online adjustments necessary during exposure, resulting in an
ultimate temporal resolution of 60 seconds. A total applied dose of 60 dpa at
the damage peak is selected for these experiments as swelling is likely to
have occurred in these systems by that dose and, with an average dose rate of
$1.7\times 10^{-3}$ dpa/sec across all exposures (corresponding to an average
ion flux of $1.9\times 10^{12}$ ions/cm2sec), irradiations could be completed
in approximately 10 hours each. Over these long exposures, then, the 1 minute
temporal resolution provides a dramatically oversampled record of the dynamic
property evolution. Prior to _in situ_ ion irradiation, samples were held at
the target temperature of 550∘C for 3–4 hours to ensure that the entire target
assembly reached thermal equilibrium. During that time, static high
temperature baseline TGS measurements were collected to provide reference
points for material properties. Measured values of thermal diffusivity for
each alloy at 25∘C and 550∘C are shown in table 1 as mean values of 6–9
measurements collected for 5000 laser shots each. Values at both temperatures
are in good agreement with temperature-dependent thermal transport data in
these systems reported by Jin and coworkers Jin  _et al._ (2017).

| Thermal Diffusivity [mm2/s] |
---|---|---
| 25∘C | 550∘C
Ni | $23.65\pm 0.36$ | $15.05\pm 0.05$
NiFe | $7.57\pm 0.04$ | $5.75\pm 0.07$
NiCoCr | $3.63\pm 0.14$ | $5.59\pm 0.31$
NiFeCoCr | $3.79\pm 0.14$ | $5.55\pm 0.19$
NiFeCoCrMn | $3.31\pm 0.10$ | $5.41\pm 0.12$
Table 1: Thermal diffusivity of the pristine CSA sample matrix at room
temperature and the temperature at which _in situ_ ion irradiation is carried
out. Figure 2: _In situ_ records of (a) SAW velocity and (b) thermal
diffusivity evolution under irradiation. Values have been normalized to the
first 5 minutes of exposure for each property set to make relative comparisons
between different alloy compositions as the initial material properties vary
by composition.

Following irradiation, cross sectional lamellae for STEM analysis were
prepared using a Thermo Fisher Scientific Scios 2 Dual Beam scanning electron
microscope with focused ion beam milling capability (SEM/FIB). A platinum
protective layer was deposited on the surface by electron beam at 30 keV which
remained intact through final thinning which was performed with 2 keV ions.
High-angle annular dark field (HAADF) STEM images were collected using an FEI
Tecnai G(2) F30 S-Twin 300 kV transmission electron microscope. STEM image
segmentation to calculate volumetric porosity is conducted using a procedure
similar to that described in Dennett  _et al._ (2018). Images are manually
thresholded using ImageJ Schneider  _et al._ (2012) and swelling calculated in
500 nm bins using the form

$S(\%)=\frac{\frac{\pi}{6}\sum_{i}d_{i}^{3}}{A\delta-\frac{\pi}{6}\sum_{i}d_{i}^{3}}\times
100,$ (1)

where $A$ is the image area analyzed, $\delta$ is the thickness of the
lamella, and $d_{i}=2(A_{i}/\pi)^{1/2}$ are the effective diameters of each
counted void determined by the void area $A_{i}$ through segmentation Dennett
_et al._ (2018); n. Yang  _et al._ (2017); Fan  _et al._ (2020). Total
swelling within the depth measured by TGS was determined using a fixed depth
of 4.54 µm and swelling for these regions was calculated over an area of 29–33
µm2. Depth-dependent swelling was calculated in these relatively large bins
due to the large void sizes observed in pure nickel. Analyzed lamella
thicknesses varied from 135 nm to 295 nm as estimated using cross-sectional
imaging during liftout.

##  III Results and Discussion

Normalized _in situ_ records of SAW velocity and thermal diffusivity evolution
in each Ni-CSA alloy are shown in fig. 2. Values are normalized to velocities
and thermal diffusivities measured during the first 5 minutes of exposure to
enable relative comparisons between materials with differing elastic moduli
and thermal transport. Examples of raw, time-domain TGS measurements from
roughly halfway through each exposure are shown in Supplementary Fig. S2. The
continuous records of both ion flux recorded during irradiation and the
surface-measured sample temperature are provided in Supplementary Fig. S3.

The dynamic evolution in SAW velocity shown in fig. 2(a) is observed to vary
significantly between the alloy compositions studied here. Relevant
expectations for this evolution can be drawn from the prior work of Dennett
and coworkers in model FCC systems undergoing void swelling through both _ex
situ_ , post-irradiation analysis Dennett  _et al._ (2018) and _in situ_
irradiation Dennett  _et al._ (2019, 2020). In these conditions, an initial
buildup of small interstitial clusters (and their interaction with any native
dislocation network) is expected to increase the elastic moduli, thereby
increasing the observed SAW velocity. In model systems, this initial increase
is then shown to transition to a void-dominated regime where the induced
volumetric porosity serves to decrease the effective modulus and thereby
reduce the SAW velocity. In Ni-Fe containing alloys, work by Barashev and
coworkers suggest similar behavior should be observed here as low-dose defect
accumulation is dominated by interstitial-type loop formation Barashev  _et
al._ (2019). Variations of these behaviors are observed across alloy
compositions. In pure Ni, no initial SAW velocity increase is observed,
indicating swelling accumulation begins immediately upon irradiation. For
NiFe, a monotonic increase is observed, indicating that across these
conditions the response remains dominated by interstitial-type cluster
formation. In NiCoCr, a rapid initial drop likely associated with transient
vacancy supersaturation buildup is following by a stiffening period, and
finally a dramatic reduction period where a void-dominated microstructure has
developed. The behavior in NiFeCoCr is similar to that of NiCoCr, albeit with
weaker relative response. Data for NiFeCoCr show more scatter in both SAW
velocity and thermal diffusivity than other materials due to the reduced
surface quality of this sample compared to others in the matrix. This results
in a reduced single-to-noise ratio as shown in Supplementary Fig. S2. Finally,
for NiFeCoCrMn, a direct entry to a stiffening regime is then followed by the
turnover expected as a result of void build-up.

Previous investigations by Dennett and coworkers suggest that a rough
determination of the “incubation dose” for void swelling could be estimated by
the transition from interstitial-dominated stiffening to void-dominated
softening behavior Dennett  _et al._ (2018, 2019, 2020). By linearly fitting
the ‘rising’ and ‘falling’ segments of the SAW evolution immediately
surrounding the stiffening-softening transition, as estimate for the
incubation dose for each alloy composition may be made. An example of this
segment analysis is shown in Supplementary Fig. S4 for NiFeCoCrMn and the
resulting incubation doses are listed in table 2 for each alloy except NiFe,
which by this acoustic metric does not exhibit significant swelling. While the
chemically complex alloys show a significantly delayed transition into
swelling, pure Ni in these conditions shows no tolerance and begins swelling
immediately upon exposure. Developing physics-based models with which the
incubation dose may be determined from _in situ_ SAW evolution is of high
priority for further investigations.

| Incubation Dose [dpa]
---|---
Ni | 0
NiFe | n/a
NiCoCr | 9.3
NiFeCoCr | 12.8
NiFeCoCrMn | 11.0
Table 2: Estimated “incubation dose” from _in situ_ SAW evolution. Pure Ni
begins swelling immediately upon the initiation of irradiation by this
acoustic metric.

In contrast to the rich behavior exhibited through changes in elastic
performance, the thermal diffusivity as shown in fig. 2(b) is observed to
change relatively little under these conditions with a notable exception. Ni
and NiFe show no discernible change in thermal performance under these
conditions. Data for NiFeCoCr suffer from low signal-to-noise and no
conclusions can be drawn from these data. NiFeCoCrMn, in contrast, shows a
notable reduction in thermal transport in these conditions up to a total
reduction of $\sim$5% at 60 dpa. A similar, much weaker, trend of decreasing
thermal diffusivity is suggested for NiCoCr, however the scatter in the data
preclude any firm determination of the total relative change. In pure metallic
systems dominated by electron thermal transport, little change is expected in
the high-temperature thermal diffusivity in the presence of lattice defects
for several factors including weak scattering of electrons from decreased
electron-phonon coupling at high temperatures Hofmann  _et al._ (2015b) and
the length scale of voids becoming much greater than the electron mean free
path Dennett  _et al._ (2019). In contrast, phonons are known to scatter
strongly from a variety of lattice defects. Of the alloys studied here, the
relative contribution of lattice thermal conductivity has been shown to
increase continually with increasing chemical complexity, with lattice thermal
conductivity contributing approximately half of the total conductivity in
NiFeCoCrMn Jin and Bei (2018); Chou  _et al._ (2009). In this light, our
observation that NiCoCr potentially shows a weak dependence of thermal
diffusivity upon irradiation and NiFeCoCrMn shows a much stronger reduction is
consistent with expectations based on relative electron and phonon
contributions. Another factor which could play a role in the strong reduction
in NiFeCoCrMn is the relatively high mobility of Mn Vaidya  _et al._ (2018)
and it’s tendency towards segregation to free surfaces Wynblatt and Chatain
(2019), which may be accelerated under irradiation conditions. Similar to
previous work by Yang and coworkers n. Yang  _et al._ (2019), phase
decomposition from gross chemical segregation is not observed in post-exposure
STEM, although Fan and coworkers have identified chemical gradients in as-
irradiated NiFeCoCr under similar conditions Fan  _et al._ (2021). As such,
local enrichment of Mn towards the free material surface under high-vacuum and
irradiation conditions, coupled with the nearer-surface sensitivity to thermal
transport in TGS measurements – sampling a depth of 1.4 µm as compared to the
4.5 µm sampled by the SAW – may play a role in the observed degradation in
thermal conductivity compared to the initially equiatomic lattice.

Figure 3: HAADF-STEM imaging of post-irradiation microstructures for all
alloys. The image depths for Ni, NiFe, and NiCoCr are equal to the transient
grating wavelength. However, since large-scale defect accumulation is observed
below this depth for the 4 and 5 component alloys, their micrographs have been
extended to capture the entire region which experienced void swelling.

HAADF-STEM micrographs of post-irradiation microstructure for all five alloy
compositions are shown in fig. 3. For Ni, NiFe, and NiCoCr, the length scale
of the resulting microstructure is found to be contained within the 4.5 µm
surface layer measured using _in situ_ TGS. For NiFeCoCr and NiFeCoCrMn, this
affected depth is found to extend beyond that of the direct applied
displacement damage from the ion beam. This behavior has been repeatedly noted
in these CSA systems Fan  _et al._ (2020); Barashev  _et al._ (2019); n. Yang
_et al._ (2017), the most distinct example of which observed here is the
presence of a fine layer of voids in NiFeCoCr just below the peak damage
location at approximately 4 µm. Segmentation of HAADF images following eq. 1
is used to produce the depth-dependent void swelling in these materials as
shown in fig. 4(a). In addition, the total swelling for the strictly the 4.5
µm surface region responsible for the observed SAW response is calculated in
fig. 4(b). For all alloys except NiFeCoCrMn, this 4.5 µm region captures the
majority of the observed void density. Voids in pure Ni are characteristic of
those expected in pure metals, namely large voids hundreds of nanometers in
diameter exhibiting sharp facets defined by local surface energies Dennett
_et al._ (2018); n. Yang  _et al._ (2017).

General differences including a finer distribution of voids in more chemically
complex alloys and the relative ordering of total volume swelling,
particularly with the performance of binary NiFe on par with that of the
quaternary and quinary alloys, are also consistent with previous works n. Yang
_et al._ (2017); Jin  _et al._ (2016). Despite these similarities in general
trends with prior works using 3 MeV Ni ions to impose lattice damage, the
total volume swelling for irradiations with 31 MeV Ni ions here is notably
lower. For example, in NiFeCoCr, recent work by Fan and coworkers observed
volume porosity of $\sim$1.2% when irradiated at 580∘C to 54 dpa peak Fan  _et
al._ (2020), while here we observe only 0.14% porosity when irradiated at
550∘C to 60 dpa peak. Differences in the relative contribution of electronic
and nuclear stopping between low (3 MeV) and high (31 MeV) energy ions are
most likely responsible for this large-scale microstructure difference.
Sellami et al. have shown that energy deposited through electronic stopping of
Ni ions into several Ni-based CSAs has the ability to reduce local strain and
anneal pre-seeded defects from low energy ion irradiation Sellami  _et al._
(2019), and “defect healing” through high energy ion implantation has been
observed in many non-metal systems Zhang and Weber (2020). The synergistic
effect of electronic energy deposition and defect generation in the high-
energy implantations carried out here results in the dramatically reduced
total swelling.

Figure 4: (a) Depth distribution and (b) total volumetric swelling measured in
each alloy post-irradiation. Total volume swelling values are averaged only
over the TGS interrogation region defined by the grating wavelength and
indicated in (a) as a dashed vertical line.

In noting the total end-state swelling observed in each of these alloys, it is
evident that the STEM-measured volumetric swelling and the total reduction in
SAW velocity measured using TGS are not directly correlated. The total volume
swelling in Ni is 1.1% while the total swelling in NiCoCr is only 0.17%.
However, the final reduction in SAW velocity in Ni is 0.2% while that in
NiCoCr is approximately 1.1%. Features other than those observable with this
magnification of STEM imaging are playing a major role in the overall dynamic
response of the elastic performance. Two lower-length-scale microstructural
features most likely play a role in the differences observed here. Some Ni-
CSAs, notably NiCoCr, are known to undergo short range chemical ordering (SRO)
upon moderate temperature annealing Zhang  _et al._ (2020) or irradiation
Zhang  _et al._ (2017). However, recent acoustic measurement of NiCoCr in both
a homogenized condition and a condition bearing significant SRO showed that
the effective elastic modulus should increase from the homogenized to ordered
conditions Zhang  _et al._ (2020), such that any ordering present in these
conditions would serve the effect of increasing the SAW velocity, opposite of
the observed larger-magnitude drop.

The most likely cause of this disproportionate reduction is therefore the
retention of a significant density of nanoscale vacancy clusters and mono-
vacancies below the STEM resolution limit which serve the same role as larger-
scale porosity and reduce the effective elastic modulus Dienes (1952). Prior
experiments targeted towards high-temperature void swelling in these systems
have shown much finer void size distributions in the ternary and quaternary
alloys under investigation n. Yang  _et al._ (2017); Fan  _et al._ (2020),
consistent with our observations in fig. 3. However these studies are also
unable to capture nanoscale vacancy clusters which are expected are strongly
influencing the modulus. A heuristic argument for the presence of these small
clusters can be made from the void size distributions for each alloy shown in
Supplementary Fig. S5, where the distributions for NiCoCr and NiFeCoCr are
clearly missing the tails of the size distribution towards small sizes, cut
off by the minimum-detectable void diameter of 18 nm in this analysis. Further
evidence for the existence of nanoscale clusters in these particular
compositions is provided computationally by Wang and coworkers, who predict
alloys of increasing chemical complexity should retain more smaller vacancy
clusters by thermodynamic analysis Wang  _et al._ (2017). Experimental results
from Tousmisto and coworkers on a similar selection of alloys up to quaternary
compositions under room-temperature ion irradiation also show that increasing
chemical complexity results in more small vacancy cluster retention using
positron annhilaition spectroscopy Tuomisto  _et al._ (2020). The weaker
acoustic response observed in NiFeCoCrMn in combination with the void size
distribution in Fig. S5 suggest that nanoscale voids are contributing
minimally in the quinary system, highlighting the unique role oversized Mn
atoms play on kinetic defect behavior.

That mono-vacancies and clusters on the smallest scales play such a dramatic
role in the material properties accessed through TGS experiments motivates a
re-examination of the common definition of swelling as provided in eq. 1 and
used throughout the literature on long-timescale radiation-induced evolution.
This value as computed through _ex situ_ microscopy analysis clearly fails to
capture the the entire spectrum of defect morphologies which may be considered
“swelling.” Indeed, the literature commonly differentiates “lattice swelling”
at the nanoscale Tuomisto  _et al._ (2020), normally captured using X-ray
diffraction Gao  _et al._ (2019), and “void swelling” at the mesoscale, the
type of volume porosity captured here through electron microscopy, as separate
effects. However, as evidenced through local elasticity, these different
scales of vacancy-type lattice defects impose the same fundamental changes on
resulting properties. As such, total swelling incubation doses identified
through _in situ_ TGS experiments may be more representative of the
irradiation dose required to achieve breakaway behavior as effects from the
entire spectrum of defect sizes and morphologies are now in fact captured.
These integrated observations of the role of defects across length scales on
bulk materials provide new insight into the dynamics of swelling and
microstructure evolution under extremes beyond traditional microscopy.

##  IV Conclusions

In summary, rapidly-developing _in situ_ laser-based methods allow
unprecedented access to the dynamic evolution of bulk materials under extreme
irradiation conditions. The thermophysical properties measured using TGS
during ion irradiation capture the integrated effects of microstructure and
defect evolution across length scales. Experiments carried out here on a
series of Ni-based CSAs demonstrate a characteristic stiffening-to-softening
transition when small-scale interstitial-type defects and loops generated at
the early stages of irradiation become dominated by vacancy-type clusters and
large voids, indicating a transition into a free swelling regime.
Interstitial-type defect buildup in binary NiFe is sufficient to dominate the
elastic response to high doses where post-irradiation STEM confirms voids have
formed, while nanoscale vacancy cluster formation in ternary NiCoCr leads to a
significant reduction in the measured acoustic wave velocity. Thermal
transport properties are minimally affected under these conditions for alloys
with low phonon contributions to thermal conductivity, Ni and NiFe, with clear
thermal performance degradation observed in NiFeCoCrMn where approximately
half of the total conductivity is contributed by the lattice. While the
lattice contribution to conductivity of the subset of Ni-CSAs studied here
increases with increasing chemical complexity, this is not generally true
across materials in this class, requiring foreknowledge of thermal carrier
partitioning to be able to predict radiation performance. Given both the non-
homogeneous distribution of lattice damage from high-energy ions and the non-
homogeneous elastic and thermal sampling imposed through TGS property
evaluation, a careful consideration of all relevant length scales must be made
when designing _in situ_ experiments. Future work should be aimed at making
quantitative correlations to determine the representative dose sampled by the
imposed thermoelastic excitation. With sensitivity to defects on the smallest
scales in bulk materials, these emerging types _in situ_ experiments are
poised to be provide unique insight into material dynamics under extremes.

###### Acknowledgements.

The authors would like to thank Dan Buller for his assistance in conducting
_in situ_ irradiation experiments. This work was supported through the INL
Laboratory Directed Research & Development Program under U.S. Department of
Energy Idaho Operations Office Contract DE-AC07-05ID14517. This work was
supported, in part, by the the DOE NNSA Stewardship Science Graduate
Fellowship under cooperative agreement No. DE-NA0002135 and the MIT-SUTD
International Design Center (IDC). This work was supported, in part, by the
U.S. Department of Energy, Office of Nuclear Energy under DOE Idaho Operations
Office Contract DE-AC07-05ID14517 as part of the Nuclear Science User
Facilities. This work was performed, in part, at the Center for Integrated
Nanotechnologies, an Office of Science User Facility operated for the DOE
Office of Science. Sandia National Laboratories is a multimission laboratory
managed and operated by National Technology & Engineering Solutions of Sandia,
LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S.
DOE’s National Nuclear Security Administration under contact DE-NA-0003525.
M.P.S. acknowledges funding from the US Nuclear Regulatory Commission’s MIT
Nuclear Education Faculty Development Program under Grant No. NRC-
HQ-84-15-G-0045. H.B. and Y.Z. were supported as part of Energy Dissipation to
Defect Evolution (EDDE), an Energy Frontier Research Center funded by the U.S.
Department of Energy, Office of Science, Basic Energy Sciences under contract
number DE-AC05-00OR22725. The views expressed in this article do not
necessarily represent the views of the U.S. DOE of the United States
Government.

## Data availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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# Inequitable Access to EV Charging Infrastructure

hak369  Hafiz Anwar Ullah Khan, , Sara Price, Charalampos Avraam, and Yury
Dvorkin

(November 2020)

###### Abstract

Access to and affordability of electric vehicle (EV) charging infrastructure
are the two prominent barriers for EV adoption. While major efforts are
underway in the United States to roll-out public EV charging infrastructure,
persistent social disparities in EV adoption call for interventions. In this
paper, we analyze the existing EV charging infrastructure across New York City
(NYC) to identify such socio-demographic and transportation features that
correlate with the current distribution of EV charging stations. Our results
demonstrate that population density is not correlated with the density of EV
chargers, hindering New York’s EV adoption and decarbonization goals. On the
contrary, the distribution of EV charging stations is heavily skewed against
low–income, Black–identifying, and disinvested neighborhoods in NYC, however,
positively correlated to presence of highways in a zip code. The results
underscore the need for policy frameworks that incorporate equity and justice
in the roll-out of EV charging infrastructure.

##  I Introduction

Transportation is a major source of greenhouse gas emissions and air
pollution, with emissions from light-duty vehicles constituting its major
share. For example, the light-duty vehicles in New York City (NYC) emit 80% of
the city’s total transportation emissions [1]. Electrified transportation is
one of the critical aspects of the global trend towards decarbonization. With
light-duty electric vehicle (EV) prices rapidly declining to as low as $18,875
[2] (after United States (US) federal tax credits and state rebates [3]) and
their ranges expanding to 400 miles [4], it is anticipated that access to
charging infrastructure will become the most prominent adoption barrier for
EVs. The significance of the availability and affordability of charging
infrastructure for adopting EVs is difficult to understate. From a planning
perspective, insufficient EV charging infrastructure manifests itself in
suppressed EV demand, discouraging private sector investments in EV charging.
Thus, public investments and policy incentives are required for seeding EV
charging infrastructure market [1]. Similarly, from the consumers’
perspective, the availability of public EV charging is an important factor in
decisions for EV purchases in the US [5]. For instance, a 2017 online survey
of US EV owners found that public charging and access to fast charging were
viewed as top criteria when buying an EV [6]. In line with [6], the survey in
[7] determines that a “lack of charging facilities in my area” was the third-
ranked reason for not purchasing an EV and a “lack of quick charging stations”
the fourth. Thus, access to EV charging infrastructure shares a symbiotic
relationship with EV adoption, and subsequently with the global
decarbonization efforts. Therefore, the problem of access to and affordability
of public EV charging infrastructure is critical for all stakeholders in EV
roll-out, including investor-owned charging companies, electric power
utilities, consumers, and regulators.

To alleviate the accessibility and affordability barriers in charging
infrastructure and spur investments in EV adoption, the US government proposes
an ambitious $7.5 billion plan for installing 500,000 EV charging stations
across the US by 2030 [8, 9]. Similarly, many states in the US have embarked
on programs for deploying public EV charging infrastructure. For example, Con
Edison, an electric power utility in NYC, will install the first 100 curbside
EV charging ports in 2021, under the New York Reforming the Energy Vision
(NYREV) program [10]. In the same year, Kansas City, Missouri, plans to
install 30 to 60 EV chargers under its Right-Of-Way project [11]. Other
curbside EV charging station projects are underway in California, Washington,
New Jersey, and Ohio [12, 13]. However, these deployments are limited in size
and do not close the constantly growing charging-capacity gap [14]. Moreover,
accessibility of EV charging infrastructure is redundant if it is not
affordable. Therefore, any roll-out of public EV charging infrastructure
should ensure that its costs and benefits are equitably distributed in the
society. Currently, the burden of this roll-out disproportionately affects
low– and middle–income, underrepresented, and disadvantaged communities,
exacerbating the already present racial, financial, and cumulative social
disparities in EV adoption [15]. Hence, as governments reconcile
decarbonization efforts and policy with environmental justice, it is
imperative that equitable access to EVs, catalyzed by EV charging
infrastructure, is ensured [16].

Current literature addresses some aspects of equitable transition towards
electrified transportation and disparities in access to EV charging
infrastructure across race and income. For instance, Cheyne et al. conclude
that disadvantaged and minority communities are disproportionately affected by
environmental and transportation injustice [17]. Hardman et al. extend these
results by showing that the current EV charging infrastructure is not
equitably dispersed and EV incentives do not support low–income buyers. This
skews the EV buying power towards predominantly white, male, high-income, and
educated households [18]. Similarly, lack of access to EV charging
infrastructure near multi-unit housing units (mostly inhabited by low-income
communities) is a key barrier in EV adoption [19]. A census block group–level
analysis in California shows that Black– and Hispanic–majority neighborhoods
have lower access to public EV charging infrastructure [20]. Brockway et al.
investigate the effects of grid limits on the growth and adoption of
Distributed Energy Resources (DERs) in the service territories of California’s
Pacific Gas and Electric (PG&E) and Southern California Edison (SCE). Results
demonstrate that a high correlation exists between race and grid limits in
these regions, such that in Black–identifying and disadvantaged communities,
hosting capacity [21] for DERs drastically decreases [15], hindering EV
adoption in these neighborhoods. Although, existing literature caters to the
socio-demographic and census block group–based analysis of equitable
distribution of EV charging infrastructure, it mainly focuses on qualitative
discussions [18] or data-driven analysis of isolated socio-economic factors
[15, 19, 20]. To the best of authors’ knowledge, a systematic analysis of
correlations between socio-demographic features and their mutual effect on the
access and affordability of EV charging infrastructure is missing. Moreover,
the analyses in this paper are carried out with a zip code–level granularity,
which is aptly suited for an urban justice setting.

In this paper, our hypothesis is that the distribution of EV charging stations
is closely related to the inter-dependent socio-demographic features of
population. We further hypothesize that features of the local transportation
landscape may also be related to the distribution of EV charging stations. For
instance, owing to a high influx of traffic, zip codes with high
concentrations of major roadways may be more desirable locations for charging
stations. Hence, the identification and quantification of such features is of
paramount importance. We consider socio-demographic features like population
size, median household income, poverty rate, and racial makeup of population,
and transportation features like presence of highways and number of highways
in each zip code. These features serve as markers to the current imbalances in
the accessibility and affordability levels of EV charging stations in the
society [22]. In this paper, we do not seek to furnish causal claims, however,
identify correlations that exist in data so that targeted policy interventions
can be designed to facilitate an equitable roll-out of EV charging
infrastructure.

##  II Data

To determine the socio-demographic and transportation factors affecting the
distribution of EV charging stations in NYC, we use the publicly available
Alternative Fuel Station Locator dataset from Alternative Fuel Data Centre at
the US Department of Energy [23]. This dataset provides a current accounting
of the types and locations of all alternative fuel stations in NYC. For this
analysis, we include only electric charging stations and exclude those
providing other alternative fuels, like biodiesel, compressed natural gas
(CNG), or liquefied natural gas (LNG). Each data point in the EV charging
station dataset corresponds to one station, irrespective of the number of EV
service equipment ports (charging outlets) and the type of connectors. The
data comprises charging stations operated by major EV charging companies in
the US, including Blink, ChargePoint, Electrify America, EVgo, FLO, Greenlots,
OpConnect, Tesla, SemaConnect, and Webasto, however, does not include
residential EV charging locations. Similarly, we obtain the demographic data
of NYC from the American Community Survey (ACS) [24]. We use ACS 1–year
estimates data profiles for 2019, which includes features of median household
income, poverty rate, and population percentage of different racial groups by
zip code. Using the NYS Streets data from the New York State (NYS) GIS
Offices, we obtain the routes and spatial information of major roadways, which
include interstates, interstate connections, state touring routes and
connectors, state 900 routes, US highways, and US highway business routes and
connectors [25], in NYC. The transportation information is then mapped to
individual zip codes of NYC, shown in Fig. 1, using the zip code boundaries
dataset from the Department of Information Technology & Telecommunications
[26]. The socio-demographic and transportation data used in this paper is
available in [27].

##  III Methods

Figure 1: Map showing the five constituent boroughs of NYC, along with the
commercial and non-commercial traffic routes (highways).

We perform correlation analyses, in Section IV-A, to identify features in the
demographic and highway datasets that impact the distribution of EV charging
stations in NYC. To this end, we define the following two target features:

  1. 1.

A binary variable representing the presence of at least one EV charging
station in a particular zip code

  2. 2.

The total number of EV charging stations in each zip code

Moreover, we test the hypotheses in Section I by defining two groups in our
dataset, such that all zip codes with at least one EV charging station
constitute one group whereas the remaining zip codes constitute the other
group. Across the five boroughs of NYC, shown in Fig. 1, there are 180 zip
codes with accompanying demographic data from the ACS [24]. 100 of these zip
codes have at least one EV charging station and 80 have no EV charging
stations. Hence, group 1 in our dataset comprises 100 data points, whereas
group 2 contains 80 data points. Owing to a normal distribution of EV charging
station data and an almost equal sample size of the two data groups, we use
t-test as a hypothesis testing tool, in Section IV-B, to compare the average
values of the two groups [28]. Our null hypothesis assumes that means of the
two data groups are equal, i.e., there are no statistical differences between
the two groups. The null hypothesis implies that the socio-demographic
features do not affect the presence of EV charging stations in zip codes,
rendering the two groups statistically identical. We use both p-value and
t-value to assess the likelihood to reject the null-hypothesis. In this case,
we use the p-value $\leq 0.05$ as statistically significant [29], indicating a
strong evidence against the null hypothesis. On the contrary, for significance
level ($\alpha$) = 0.05, t-value is significant if $\mid\textit{t}\mid\geq
1.96$.

While correlations can be identified between individual demographic features
and distribution of EV charging stations in NYC, the inter-dependency of these
features cannot be ruled out. For example, the median household income of a
particular zip code may or may not be related to the racial makeup of its
population. Therefore, we analyze the dependency between socio-demographic
features using conditional analysis in Section IV-C. The number of EV charging
stations in each zip code is analyzed as a function of the percentage of
population identifying as white or non–white, conditioned on a threshold
income. We choose this threshold as the annual median income of NYC for
2015–2019, which is estimated to be $64,000 [24].

##  IV Case Study

Figure 2: Heat map depicting the zip code–level population density in NYC,
based on data in [24].

The case study focuses on NYC, with Fig. 1 showing its five constituent
boroughs – Manhattan, Bronx, Queens, Brooklyn, and Staten Island – in
different colors. In this section, we use the demographic and EV charging
station data with a zip code resolution, described in Section II, to retrieve
correlations between different demographic features and the distribution of EV
charging stations across NYC. Hypothesis testing is performed between the set
of zip codes with at least one EV charging station and the set of zip codes
with no EV charging stations to ascertain the features that distinguish these
two sets. Finally, to understand the inter-dependencies of demographic
features, we use conditional analysis to see the distribution of EV charging
stations in different zip codes of NYC.

Using data from [24], we show the population density in each zip code of NYC
in Fig. 2. We note that the population density in NYC is neither uniform
across zip codes nor across the five boroughs. Using Figs. 1 and 2, we observe
that Brooklyn has the highest population density (shown in yellow in Fig. 2)
whereas average population density is very low in Staten Island and Manhattan.
Similarly, using the EV charging station data in [23], we show the
distribution of EV charging stations in NYC on a zip code level, in Fig. 3. We
note that the distribution of EV charging stations in heavily non-uniform
among different boroughs such that the maximum number of charging stations are
concentrated in Manhattan, whereas Bronx, Queens, and Brooklyn have little to
no charging stations in most of the zip codes.

Figure 3: Zip code–level distribution of EV charging stations in NYC, based on
data in [23].

As an initial hypothesis, we compare the trends in population density in zip
codes and boroughs to the associated distribution of EV charging stations.
Comparing Figs. 2 and 3, we note that there exists a huge disparity between
the distribution of EV charging stations and population density in NYC. While
geographical areas (multiple contiguous zip codes) in Brooklyn have some of
the highest population densities, the same areas have very few EV charging
stations. Similarly, most of the EV charging stations are concentrated in
Manhattan, where population density is one of the lowest. This indicates that
population density is not a good indicator for the distribution of EV charging
stations, underscoring inaccessibility of residential EV charging
infrastructure as an acute barrier to EV adoption. Thus, further analysis of
socio-demographic data is required to capture features that determine the
presence and accessibility of EV charging stations. In the following sections,
we analyze the demographic characteristics that correlate with the development
and allocation of EV charging stations in NYC.

###  IV-A Correlation Analysis

TABLE I: Correlation between demographic/transportation features and the target features of whether an EV charging station is present and the number of EV charging staions in a zip code. Demographic Feature |  Station Present |  No. of Stations
---|---|---
Median household income |  0.45 |  0.58
White–identifying population (%) |  0.43 |  0.43
Highway present |  0.32 |  0.23
Asian–identifying population (%) |  0.24 |  0.16
Highway count |  0.2 |  0.07
Poverty rate |  0.2 |  0.01
Hispanic–identifying population (%) |  0.18 |  -0.06
Black–identifying population (%) |  -0.02 |  -0.14

Table I shows the results of the correlation analysis. Median household income
and percentage of White–identifying population in a zip code show the highest
positive correlation with the presence of at least one EV charging station and
the number of stations present in that zip code. Hence, higher the median
income of a given zip code, the higher the probability that at least one EV
charging station will be present in that zip code. Similarly, a higher median
income also implies a higher number of EV charging stations in a zip code. The
same pattern holds when we compare the relationship between the percentage of
White–identifying population in each zip code and the two aforementioned
target features. This trend can be visualized using Fig. 4, which shows that
zip codes in Manhattan have the highest median household income. These zip
codes also have the highest number of EV charging stations, as given by a
correlation coefficient of 0.58 in Table I. Similarly, Bronx has the lowest
median income and the lowest number of EV charging stations. We note in Table
I, that the correlation coefficient between percentage of White–identifying
population and the presence of EV charging stations is smaller as compared to
the one between median household income and presence of EV charging stations.
This can be explained using Fig. 5, where some zip codes in Manhattan have a
notably high percentage of White–identifying population (and a high median
household income) and a high number of EV charging stations. However, the
trend does not hold in Staten Island and large portions of Brooklyn, which
have similarly high percentages of White–identifying population but a very low
penetration of EV charging stations. We also observe a weak positive
correlation of 0.32 between the presence of highways in a zip code and the
number of EV charging stations present in that zip code.

Hence, although the percentage of White–identifying population is a good
indicator for predicting the distribution of EV charging stations across zip
codes in NYC, certain regions in Staten Island and Brooklyn do not follow this
correlation. However, median household income explains the distribution of EV
charging stations throughout NYC.

Figure 4: Distribution of household income in NYC by zip code, based on data
in [24]. Figure 5: Percentage of White–identifying population in NYC by zip
code, based on data in [24].

###  IV-B Hypothesis Testing

Based on the two data groups defined in Section III, we perform a two-sample
t-test between these two populations for different demographic and
transportation features to determine (dis)similarities between the two groups.
Table II shows the results of this analysis along with the mean and median
values of the features for each group. The mean values for median household
income and percentage of White–identifying population for zip codes with at
least one charging station are significantly higher than for zip codes without
any charging station. Meanwhile, the mean value for percentage of
Black–identifying population is significantly lower in zip codes with at least
one charging station versus those without any.

TABLE II: Results of hypothesis testing between the group of zip codes with and without EV charging stations. Demographic Feature | Mean | Median |  t-stat |  p-value
---|---|---|---|---
|  Station |  No Station |  Station |  No Station |  |
Median household income |  112,000 |  78,300 |  87,242 |  75,471 |  4.02 |  .000087
Poverty rate |  15.39 |  17.29 |  13.18 |  13.78 |  -1.21 |  .23
Percentage of White–identifying population |  51.79 |  39.08 |  56.37 |  37.01 |  3.36 |  .00094
Percentage of Black–identifying population |  16.79 |  29.12 |  7.26 |  22.05 |  -3.37 |  .00094
Percentage of Hispanic–identifying population |  25.06 |  27.79 |  17.05 |  19.94 |  -0.93 |  .35
Percentage of Asian–identifying population |  15.81 |  13.95 |  10.48 |  7.25 |  0.87 |  .39
Highway count |  1.79 |  1.20 |  2 |  0.5 |  -0.83 |  .41
Highway present |  0.81 |  0.50 |  1 |  0.5 |  5.15 |  .00000056

Based on the results of two-sample t-test, reported in Table II, we observe
that median household income, percentage of White–identifying population,
percentage of Black–identifying population, and presence of highways in zip
codes offer significant t-values and p-values. Hence, using the p-values, we
can reject the null hypothesis for these features, concluding that the means
of the two groups of zip codes are not equal, indicating that there are
significant statistical differences between the two groups. Similarly, the
same features have significant t-values, indicating that the two groups of zip
codes are dissimilar from one another.

Our analysis concludes that presence of highways is the most significant
feature that distinguishes the two data groups, followed by median household
income, and percentages of White– and Black–identifying population. The
results complement the trends observed in correlation analysis, and offer
critical insights into demographic features that determine the distribution of
EV charging stations across NYC.

Figure 6: Conditional analysis of percentage of non-White-identifying
population and the number of EV charging stations in a zip code, conditioned
on median income of NYC.  Figure 7: Conditional analysis of percentage of
White-identifying population and the number of EV charging stations in a zip
code, conditioned on median income of NYC.

###  IV-C Conditional Analysis

Figs. 6 and 7 show the results of conditional analysis where we identify the
existence of conditional trends. We see that in zip codes with median income
greater than $64,000, there is a clear positive correlation between the number
of EV charging stations and the percentage of White–identifying population.
Similarly, in zip codes with median income less than or equal to $64,000, a
negative correlation exists between the number of EV charging stations and the
percentage of non-White–identifying population. These results show that
although the distribution of EV charging stations in NYC can be correlated to
individual features of dataset, a better understanding of EV charging
infrastructure is acquired by intersecting economic and racial profiles of
population.

##  V Conclusion

This paper analyzes the socio-demographic and transportation features that
affect the distribution of EV charging stations in NYC. Based on correlation
analysis, hypothesis testing, and conditional analysis, our results
demonstrate that the availability and affordability of EV charging stations in
NYC are not determined by the population density, but are correlated with the
median household income, percentage of White–identifying population, and
presence of highways in a zip code. The current distribution is heavily skewed
against low–income, Black–identifying, and disadvantaged neighborhoods. The
existing inequities in EV infrastructure, coupled with underdeveloped
electricity, transportation, or communication infrastructures in vulnerable
communities, may result in biased and inequitable siting decisions for future
EV charging infrastructure roll–out. Therefore, justice–centric policy
frameworks are imperative to ensure large-scale and equitable EV adoption.

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