U.S. patent application number 15/475807 was filed with the patent office on 2017-10-05 for modeling of nanoparticle agglomeration and powder bed formation in microscale selective laser sintering systems.
The applicant listed for this patent is Board of Regents, The University of Texas System. Invention is credited to Michael A. Cullinan, Nilabh Kumar Roy, Anil Yuksel.
Application Number | 20170282247 15/475807 |
Document ID | / |
Family ID | 59960647 |
Filed Date | 2017-10-05 |
United States Patent
Application |
20170282247 |
Kind Code |
A1 |
Cullinan; Michael A. ; et
al. |
October 5, 2017 |
MODELING OF NANOPARTICLE AGGLOMERATION AND POWDER BED FORMATION IN
MICROSCALE SELECTIVE LASER SINTERING SYSTEMS
Abstract
Exemplified microscale selective laser sintering (.mu.-SLS or
micro-SLS) systems and methods facilitate modeling of the
nanoparticle powder bed by simulating the interactions between
particles during the powder spreading operation. In particular, the
exemplified methods and system use multiscale modeling techniques
to accurately predict the formation and mechanical/electrical
properties of parts produced by selective laser sintering of powder
beds. Discrete element modeling is used for nanoscale particle
interactions by implementing the different forces dominant at
nanoscale. A heat transfer analysis is used to predict the
sintering of individual particles in the powder beds in order to
build up a complete structural model of the parts that are being
produced by the SLS process.
Inventors: |
Cullinan; Michael A.;
(Austin, TX) ; Yuksel; Anil; (Austin, TX) ;
Roy; Nilabh Kumar; (Austin, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Board of Regents, The University of Texas System |
Austin |
TX |
US |
|
|
Family ID: |
59960647 |
Appl. No.: |
15/475807 |
Filed: |
March 31, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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62316644 |
Apr 1, 2016 |
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62316666 |
Apr 1, 2016 |
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62454456 |
Feb 3, 2017 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01L 21/6838 20130101;
H01L 2224/75261 20130101; B22F 2003/1056 20130101; H01L 2224/75901
20130101; H01L 2223/54426 20130101; H01L 23/4985 20130101; H01L
2224/81007 20130101; H01L 21/4857 20130101; B22F 2003/1059
20130101; H01L 23/3135 20130101; H01L 2224/81192 20130101; H01L
23/544 20130101; B33Y 50/02 20141201; B33Y 80/00 20141201; H01L
24/75 20130101; H01L 2224/75101 20130101; H01L 21/67115 20130101;
H01L 2224/83132 20130101; H01L 24/81 20130101; H01L 21/563
20130101; H01L 24/83 20130101; H01L 2224/81815 20130101; B22F
1/0044 20130101; B23K 2101/36 20180801; H01L 2224/83939 20130101;
B22F 2003/1057 20130101; B33Y 70/00 20141201; H01L 2224/9211
20130101; H01L 2224/7501 20130101; H01L 2224/81224 20130101; H01L
2224/83007 20130101; B33Y 10/00 20141201; B22F 7/02 20130101; B33Y
30/00 20141201; H01L 2224/83224 20130101; H01L 24/92 20130101; H01L
2224/81908 20130101; B22F 2999/00 20130101; B23K 1/0008 20130101;
H01L 21/4853 20130101; H01L 2224/83908 20130101; H01L 2224/81054
20130101; G06F 30/23 20200101; H01L 21/565 20130101; H01L 21/67144
20130101; Y02P 10/25 20151101; B22F 3/1055 20130101; H01L
2224/81132 20130101; H01L 2224/83054 20130101; Y02P 10/295
20151101; B22F 2999/00 20130101; B22F 3/1055 20130101; B22F 1/0018
20130101; B22F 2999/00 20130101; B22F 3/1055 20130101; B22F 1/0022
20130101 |
International
Class: |
B22F 3/105 20060101
B22F003/105; B33Y 50/02 20060101 B33Y050/02; G06F 17/50 20060101
G06F017/50; B33Y 10/00 20060101 B33Y010/00 |
Claims
1. A method of fabricating a three-dimensional workpiece, on a
layer-by-layer basis, by forming, for each layer, a uniform layer
of nanoparticle powders to be selectively sintered, the method
comprising dispensing a generally uniform layer of nanoparticle ink
or a colloid comprising a solvent having a plurality of
nanoparticles mixed or suspended therein, wherein the solvent of
the layer of colloid evaporates to produce a generally uniform
layer of nanoparticles powder on the working surface of the
workpiece.
2. The method of claim 1, wherein the nanoparticle ink or the
colloid comprises a metal particle selected from the group
consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu,
Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf,
Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm,
Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof.
3. The method of claim 1, wherein the nanoparticle ink or the
colloid has an average particle size selected from the group
consisting of about 8 nanometers (nm), about 9 nm, about 10 nm,
about 11 nm, about 12 nm, about 13 nm, about 14 nm, about 15 nm,
about 16 nm, about 17 nm, about 18 nm, about 19 nm, about 20 nm,
about 21 nm, about 22 nm, about 23 nm, about 24 nm, about 25 nm,
about 26 nm, about 27 nm, about 28 nm, about 30 nm, about 31 nm,
about 32 nm, about 33 nm, about 34 nm, about 35 nm, about 36 nm,
about 37 nm, about 38 nm, about 39 nm, about 40 nm, about 41 nm,
about 42 nm, about 43 nm, about 44 nm, about 45 nm, about 46 nm,
about 47 nm, about 48 nm, about 49 nm, about 50 nm, about 51 nm,
about 52 nm, about 53 nm, about 54 nm, about 55 nm, about 56 nm,
about 57 nm, about 58 nm, about 59 nm, about 60 nm, about 61 nm,
about 62 nm, about 63 nm, about 64 nm, about 65 nm, about 66 nm,
about 67 nm, about 68 nm, about 69 nm, about 70 nm, about 71 nm,
about 72 nm, about 73 nm, about 74 nm, about 75 nm, about 76 nm,
about 77 nm, about 78 nm, about 79 nm, about 80 nm, about 81 nm,
about 82 nm, about 83 nm, about 84 nm, about 85 nm, about 86 nm,
about 87 nm, about 88 nm, about 89 nm, about 90 nm, about 91 nm,
about 92 nm, about 93 nm, about 94 nm, about 95 nm, about 96 nm,
about 97 nm, about 98 nm, about 99 nm, and about 100 nm.
4. The method of claim 1, wherein the plurality of nanoparticles
are substantially spherical in shape.
5. A method of predicting mechanical and electrical properties of a
three-dimensional part produced by selective laser sintering of
powder beds, the method comprising: generating, via processor, a
discrete element model (DEM) comprising a plurality of elements
each corresponding to a nanoparticle, the plurality of elements,
collectively, having a size distribution, discrete element model
incorporating gravitational and van der walls forces; determining,
via the processor, a void fraction value for DEM; and determining,
via the processor, using a solver, one or more parameters that
results in a minimum value for the void fraction value, wherein the
DEM is used to account for and predict agglomeration in
nanoparticle systems.
6. The method of claim 5, comprising: importing, the discrete
element model, at steady state configuration, into a finite element
solver, wherein the finite element solver is configured to solve a
near-field energy transfer.
7. The method of claim 5, wherein the discrete element model
facilitates analysis of nanoparticle beds as a whole distribution
under dominant nanoscale force interactions.
8. The method of claim 5, wherein the discrete element model is
used in both a particle-level and a part-level analysis to create a
complete powder-to-part analysis.
9. The method of claim 5, comprising: optimizing critical
parameters for selective laser sintering process to achieve
micro-scale features.
10. The method of claim 5, comprising: optimizing critical
parameters for selective laser sintering process to achieve
sub-micron-scale features.
11. The method of claim 5, comprising: predicting, via the
processor, locations of the nanoparticle at steady state.
12. The method of claim 11, comprising: performing, via the
processor, thermal simulation using the locations of the
nanoparticle at steady state.
13. The method of claim 5, wherein the DEM model comprises a number
of spherical particles, N.sub.m, with diameter, D.sub.m, and
density, .rho..sub.sm, wherein each of the N particles is defined
within a Lagrangian reference at time t by its position,
X.sup.(i)(t), linear velocity, V.sup.(i)(t), angular velocity,
.omega..sup.(i)(t), diameter, D.sup.(i), density .rho..sup.(i), and
mass m.sup.(i); to position, linear velocity and angular velocities
of the i.sup.thparticle change with time according to Newton's laws
as: dX ( i ) ( t ) dt = V ( i ) ( t ) ##EQU00024## m ( i ) dV ( i )
( t ) dt = F T ( i ) = m ( i ) g + F d ( i ) ( t ) + F c ( i ) ( t
) ##EQU00024.2## I ( i ) d .omega. ( i ) ( t ) dt = T ( i )
##EQU00024.3## wherein a total drag force, F.sub.d(i), is found by
a summation of pressure and viscous forces, and wherein a net
contact force, F.sub.c(i), is a force acting on the particle as a
result of contact with other particles and a total force on each
particle, F.sub.T.sup.(i), is found through a summation of all
forces acting on an i.sup.thparticle.
14. The method of claim 5, wherein, for each two particles in
contact, a normal and tangential effective spring stiffness between
two particles in contact is calculated using the elastic modulus
and Poisson's ratio of the nanoparticles as: .delta. n , ij = 4 3 E
m E l r m l E m ( 1 - .sigma. l 2 ) + E l ( 1 - .sigma. m 2 )
.delta. n , ij 1 / 2 ##EQU00025## k t , ij = 16 3 G m G l r m l G m
( 2 - .sigma. l ) + G l ( 2 - .sigma. m ) .delta. n , ij 1 / 2
##EQU00025.2## wherein E.sub.mand E.sub.l are elastic moduli, and
.sigma..sub.m and .sigma..sub.l are Poisson ratios for m.sup.th and
l.sup.th nanoparticles.
15. The method of claim 5, wherein coefficients of normal
restitution matrix and tangential coefficient of restitution are
written as M.times.M symmetric matrices for M solid-phases.
16. The method of claim 5, wherein van der Waals force interaction
between two nanoparticles or between particle and a surface are
calculated using the inner and outer cutoff values of the particle
or the wall as F = AR 12 r 2 ( ( Asperities Asperities + R ) + 1 (
1 + Asperities r ) 2 ) F = 2 .pi. .PHI. R ( ( Asperities Asperities
+ R ) + 1 ( 1 + Asperities r inner cutoff ) 2 ) ##EQU00026##
wherein A is the Hamaker constant, R is an equivalent radius, r is
a separation distance, .phi. is a surface energy, D is a particle
diameter, rP.sub.inner cutoff .sup.and rP.sub.outer cutoff are the
inner and outer cutoff van der Waals values between
particle-particle interactions, asperity, h, is a general
definition of roughness and impurity on a surface, and rW.sub.inner
cutoff and rW.sub.outer cutoff are the inner and outer cutoff value
between particle-wall interactions.
17. The method of claim 5, wherein the size distribution is modeled
as a Gaussian distribution.
18. The method of claim 5, wherein the size distribution is modeled
as a log-normal distribution.
19. The method of claim 5, wherein the DEM is initially generated
by inserting a random-size particle at a random location in a
pre-defined volume until no other particles fits in the pre-defined
volume without overlapping another particle.
20. The method of claim 15, comprising: performing, via the
processor, a Neighbor Search algorithm to determine which particles
are touching or overlapping as neighbors ,wherein any two particles
i and j that are located at X.sup.(i)and X.sup.(j), and have radii
R.sub.i and R.sub.j, are considered neighbors upon satisfying
condition: |X.sup.(i)-X.sup.(j)|<K(R.sub.i+R.sub.j) wherein K is
an interaction distance constant.
21. The method of claim 5, wherein the DEM includes nanoscale heat
transfer analysis in modeling thermal properties of the powder bed
with nanoparticles.
Description
RELATED APPLICATIONS
[0001] This application claims priority to, and the benefit of,
U.S. Provisional Appl. No. 62/316,644, filed Apr. 1, 2016, title
"Micro-Selective Sintering Laser System and Method Thereof"; U.S.
Provisional Appl. No. 62/316,666, filed Apr. 1, 2016, title
"Modeling of Nanoparticle Agglomeration and Powder Bed Formation in
Microscale Laster Sintering Systems"; and U.S. Provisional Appl.
No. 62/454,456, filed Feb. 3, 2017, title "Micro-selective
Sintering Laser on Flexible Substrates and With Multi-Material
Capabilities," each of which is incorporated by reference herein in
its entirety.
BACKGROUND
[0002] Micro- and nano-scale additive manufacturing methods in
metals, plastics, and ceramics have many applications in the
aerospace, medical device, and electronics industries. For example,
the fabrication of additively-manufactured parts with micron-scale
resolutions makes possible the production of cellular materials
with controlled microstructures. Such materials can exhibit very
high strength-to-weight ratios, which is critical for a number of
applications in the aerospace industry. Similarly, the medical
industry could benefit from the additive manufacturing of metal
parts with controlled microstructures, since this process could be
used to fabricate custom implants with enhanced surface structures
to either promote or prevent the adhesion of cells to the implant
in specific areas. Similarly, controlled microstructures may be
used in a number of microelectronic packaging applications.
[0003] Selective laser micro-sintering (or micro-selective laser
sintering ".mu.-SLS" or "micro-SLS") is an additive manufacturing
technology that uses a continuous high power laser to manufacture a
three-dimensional component (e.g., a part), under condition of
vacuum or reduced shield gas pressure, in a layer-by-layer fashion
from a powder (e.g., plastic, metal, polymer, ceramic, composite
materials, etc.). That is, metal powders are spread onto a powder
bed and a continuous laser beam is scanned across the powder bed to
sinter together the metal powders at the scanned locations; a new
layer of powder is then spread onto the bed over the sintered layer
and the process is repeated to build a three-dimensional part.
[0004] There are many challenges to understanding the physics of
the process at nanoscale as well as with conducting experiments at
that scale; hence, modeling and computational simulations are vital
to understand the sintering process physics. At the sub-micron
(.mu.m) level, the interaction between nanoparticles under high
power laser heating raises additional near-field thermal issues
such as thermal diffusivity, effective absorptivity, and extinction
coefficients compared to larger scales. Thus, nanoparticle's
distribution behavior and characteristic properties are very
important to understanding the thermal analysis of nanoparticles in
a .mu.-SLS process.
[0005] Therefore, what are needed are devices, systems and methods
that overcome challenges in the present art, some of which are
described above.
SUMMARY
[0006] Exemplified microscale selective laser sintering (.mu.-SLS
or micro-SLS) systems and methods facilitate modeling of the
nanoparticle powder bed by simulating the interactions between
particles during the powder spreading operation. In particular, the
exemplified methods and system use multiscale modeling techniques
to accurately predict the formation and mechanical/electrical
properties of parts produced by selective laser sintering of powder
beds. Discrete element modeling is used for nanoscale particle
interactions by implementing the different forces dominant at
nanoscale. The given size distribution of particles with desired
boundary conditions are generated. The particles interact with each
other and when they settle down at steady state, they have a
specific location. This steady state locations are imported into a
finite element solver for the analysis of the near field energy
transfer. This heat transfer analysis is used to predict the
sintering of individual particles in the powder beds in order to
build up a complete structural model of the parts that are being
produced by the SLS process. By analyzing the near field energy
transfer and sintering for the nanoparticles which can be generated
by a given size distribution and force interaction,
mechanical/electrical properties of parts produced by selective
laser sintering of powder beds can be accurately predicted. In
addition, the cross section and a detailed particle surface
analysis such as temperature distribution are obtained.
[0007] The exemplified methods and systems facilitate the build-up
of a complete model of fabricated part including void formation
from a set of use specified input parameters. This method is unique
in that it builds up a model of the part by analyzing the
individual particles that are being sintered and building them up
into a complete model of the entire part. This is the first
technique that provides the analysis of nanoparticle beds as a
whole distribution under the dominant nanoscale force interactions.
The exemplified methods and systems takes into account the entire
sintering process for the particle level to the part level to
create a complete powder-to-part analysis.
[0008] In some embodiments, a general modeling approach is used to
better understand the formation of parts in the .mu.-SLS system.
This particle bed is then imported into a multi-physics finite
element software package where interactions between the incident
laser and the nanoparticle bed are simulated. These simulations are
used to generate a temperature profile within the particle bed as a
function of time. This temperature profile is coupled with a phase
field model of the nanoparticle morphology in a finite element
software in order to model the how the nanoparticles become
sintered together during the .mu.-SLS process. Next, a new
nanoparticle layer is added to the model and the process is
repeated until an entire part is built up. Using the results of
these simulations, a 3D model of the fabricated part can be
assembled and predictions of the electrical/mechanical properties
of the part can be made. The predictions can then be evaluated
against the measured properties of the parts produced using the
.mu.-SLS testbed. The .mu.-SLS testbed is used to validate each
step of the simulation and modeling effort.
[0009] In some embodiments, the exemplified methods and systems are
used to predict the nanoparticle's locations at steady state to be
used for thermal simulation.
[0010] In some embodiments, the exemplified methods and systems are
used to account for and predicts agglomeration in nanoparticle
systems.
[0011] In some embodiments, the exemplified methods and systems
includes nanoscale heat transfer analysis in modeling the thermal
properties of the powder bed with nanoparticles.
[0012] In some embodiments, the exemplified methods and systems are
used for optimization of the critical parameters for submicron
features.
[0013] In some embodiments, the exemplified methods and systems are
used for robust analysis providing flexible parameter
adjustment.
[0014] In some embodiments, the exemplified methods and systems are
used to create complete part models based just on the size
distribution of particles in the powder bed, the geometry of the
part and processing parameters such as laser scan speed, laser
power, layer thickness and material being sintered.
[0015] According to an aspect, a method is disclosed for
fabricating a three-dimensional workpiece, on a layer-by-layer
basis, by forming, for each layer, a uniform layer of nanoparticle
powders to be selectively sintered. The method includes dispensing
a generally uniform layer of nanoparticle ink or a colloid
comprising a solvent having a plurality of nanoparticles mixed or
suspended therein, wherein the solvent of the layer of colloid
evaporates to produce a generally uniform layer of nanoparticles
powder on the working surface of the workpiece.
[0016] In some embodiments, the nanoparticle ink or the colloid
comprises a metal particle selected from the group consisting of
Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y,
Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os,
Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy,
Ho, Er, Tm, Yb, and combinations thereof.
[0017] In some embodiments, the nanoparticle ink or the colloid has
an average particle size selected from the group consisting of
about (e.g., within .+-.0.5) 8 nanometers (nm), about 9 nm, about
10 nm, about 11 nm, about 12 nm, about 13 nm, about 14 nm, about 15
nm, about 16 nm, about 17 nm, about 18 nm, about 19 nm, about 20
nm, about 21 nm, about 22 nm, about 23 nm, about 24 nm, about 25
nm, about 26 nm, about 27 nm, about 28 nm, about 30 nm, about 31
nm, about 32 nm, about 33 nm, about 34 nm, about 35 nm, about 36
nm, about 37 nm, about 38 nm, about 39 nm, about 40 nm, about 41
nm, about 42 nm, about 43 nm, about 44 nm, about 45 nm, about 46
nm, about 47 nm, about 48 nm, about 49 nm, about 50 nm, about 51
nm, about 52 nm, about 53 nm, about 54 nm, about 55 nm, about 56
nm, about 57 nm, about 58 nm, about 59 nm, about 60 nm, about 61
nm, about 62 nm, about 63 nm, about 64 nm, about 65 nm, about 66
nm, about 67 nm, about 68 nm, about 69 nm, about 70 nm, about 71
nm, about 72 nm, about 73 nm, about 74 nm, about 75 nm, about 76
nm, about 77 nm, about 78 nm, about 79 nm, about 80 nm, about 81
nm, about 82 nm, about 83 nm, about 84 nm, about 85 nm, about 86
nm, about 87 nm, about 88 nm, about 89 nm, about 90 nm, about 91
nm, about 92 nm, about 93 nm, about 94 nm, about 95 nm, about 96
nm, about 97 nm, about 98 nm, about 99 nm, and about 100 nm.
[0018] In some embodiments, the plurality of particles are
substantially spherical in shape.
[0019] According to another aspect, a method is disclosed for
predicting mechanical and electrical properties of a
three-dimensional part produced by selective laser sintering of
powder beds, the method comprising: generating, via processor, a
discrete element model (DEM) comprising a plurality of elements
each corresponding to a nanoparticle, the plurality of elements,
collectively, having a size distribution, discrete element model
incorporating gravitational and van der walls forces; determining,
via the processor, a void fraction value for DEM; and determining,
via the processor, using a solver, one or more parameters that
results in a minimum value for the void fraction.
[0020] In some embodiments, the method includes, importing, the
discrete element model, at steady state configuration, into a
finite element solver, wherein the finite element solver is
configured to solve a near-field energy transfer.
[0021] In some embodiments, the discrete element model facilitates
analysis of nanoparticle beds as a whole distribution under the
dominant nanoscale force interactions.
[0022] In some embodiments, the discrete element model is used in
both a particle-level and a part-level analysis to create a
complete powder-to-part analysis.
[0023] In some embodiments, the method includes, optimizing
critical parameters (e.g., size distribution of particles in the
powder bed, part geometry, laser scan speed, laser power, layer
thickness, and material being sintered) for selective laser
sintering process to achieve micro-scale features.
[0024] In some embodiments, the method includes, optimizing
critical parameters (e.g., size distribution of particles in the
powder bed, part geometry, laser scan speed, laser power, layer
thickness, and material being sintered) for selective laser
sintering process to achieve sub-micron-scale features.
[0025] In some embodiments, the method includes predicting, via the
processor, locations of the nanoparticle at steady state.
[0026] In some embodiments, the method includes performing, via the
processor, thermal simulation using the locations of the
nanoparticle at steady state.
[0027] In some embodiments, the DEM model comprises a number of
spherical particles, N.sub.m, with diameter, D.sub.m, and density,
.rho..sub.sm, wherein each of the N particles is defined within a
Lagrangian reference at time t by its position, X.sup.(i)(t),
linear velocity, V.sup.(i)(t), angular velocity,
.omega..sup.(i)(t), diameter, D.sup.(i), density .rho..sup.(i), and
mass m.sup.(i); to position, linear velocity and angular velocities
of the i.sup.thparticle change with time according to Newton's laws
as:
dX ( i ) ( t ) dt = V ( i ) ( t ) ##EQU00001## m ( i ) dV ( i ) ( t
) dt = F T ( i ) = m ( i ) g + F d ( i ) ( t ) + F c ( i ) ( t )
##EQU00001.2## I ( i ) d .omega. ( i ) ( t ) dt = T ( i )
##EQU00001.3##
wherein the total drag force, F.sub.d(i), is found by the summation
of pressure and viscous forces, and wherein the net contact force,
F.sub.c(i), is the force acting on the particle as a result of
contact with other particles and the total force on each particle,
F.sub.T.sup.(i), is found through the summation of all forces
acting on the i.sup.thparticle.
[0028] In some embodiments, for each two particles in contact, a
normal and tangential effective spring stiffnesses between two
particles in contact is calculated using the elastic modulus and
Poisson's ratio of the nanoparticles as:
.delta. n , ij = 4 3 E m E l r ml E m ( 1 - .sigma. l 2 ) + E l ( 1
- .sigma. m 2 ) .delta. n , ij 1 / 2 ##EQU00002## k t , ij = 16 3 G
m G l r ml G m ( 2 - .sigma. l ) + G l ( 2 - .sigma. m 2 ) .delta.
n , ij 1 / 2 ##EQU00002.2##
wherein E.sub.mand E.sub.l are the elastic moduli and .sigma..sub.m
and .sigma..sub.l are the Poisson ratios for the m.sup.th an
dl.sup.th nanoparticles.
[0029] In some embodiments, coefficients of normal restitution
matrix and the tangential coefficient of restitution are written as
M.times.M symmetric matrices for M solid-phases.
[0030] In some embodiments, the van der Waals force interaction
between two nanoparticles or between particle and a surface are
calculated using the inner and outer cutoff values of the particle
or the wall as
F = AR 12 r 2 ( ( Asperities Asperities + R ) + 1 ( 1 + Asperities
r ) 2 ) ##EQU00003## F = 2 .pi..PHI. R ( ( Asperities Asperities +
R ) + 1 ( 1 + Asperities r inner cutoff ) 2 ) ##EQU00003.2##
wherein A is the Hamaker constant, R is the equivalent radius, r is
the separation distance, .phi. is the surface energy, D is the
particle diameter, rP.sub.inner cutoff and rP.sub.outer cutoff are
the inner and outer cutoff van der Waals value between
particle-particle interaction, and asperity, h, is the general
definition of roughness and impurity on the surface. rW.sub.inner
cutoff and rW.sub.outer cutoff are the inner and outer cutoff value
between particle-wall interaction.
[0031] In some embodiments, the size distribution is modeled as a
Gaussian distribution.
[0032] In some embodiments, the size distribution is modeled as a
log-normal distribution.
[0033] In some embodiments, the DEM is initially generated by
inserting a random-size particle at a random location in a
pre-defined volume until no other particles fits in the volume
without overlapping another particle.
[0034] In some embodiments, the method includes, performing, via
the processor, a Neighbor Search algorithm to determine which
particles are touching or overlapping as neighbors, wherein any two
particles i and j that are located at X.sup.(i) X.sup.(j), and have
radii R.sub.i and R.sub.j, are considered neighbors if they satisfy
the following condition:
|X.sup.(i)-X.sup.(j)|<K(R.sub.i+R.sub.j)
wherein K is an interaction distance constant.
[0035] In some embodiments, the void fraction value is calculated
as
Fraction = Empty Fill , ##EQU00004##
wherein
Empty = V cube - j = 1 n 4 3 .pi. r j 3 , ##EQU00005##
and wherein
V cube = ( ( max ( Position x + Diameter 2 ) - min ( Position x -
Diameter 2 ) * ( max ( Position y + Diameter 2 ) - min ( Position y
- Diameter 2 ) * ( max ( Position z + Diameter 2 ) - min ( Position
z - Diameter 2 ) ) . ##EQU00006##
[0036] In some embodiments, the DEM is used to account for and
predict agglomeration in nanoparticle systems.
[0037] In some embodiments, the DEM includes nanoscale heat
transfer analysis in modeling the thermal properties of the powder
bed with nanoparticles.
BRIEF DESCRIPTION OF THE DRAWINGS
[0038] The components in the drawings are not necessarily to scale
relative to each other and like reference numerals designate
corresponding parts throughout the several views:
[0039] FIG. 1 depicts a schematic of two particles in contact.
[0040] FIG. 2 depicts a schematic of the Spring-dashpot system.
[0041] FIG. 3 depicts a schematic view of nanoparticles in the
domain.
[0042] FIG. 4 depicts a schematic of typical Gaussian
distribution.
[0043] FIG. 5 depicts a schematic of typical log-normal
distribution.
[0044] FIG. 6 depicts the neighbor search algorithm for
"cell-linked list" in 2D scheme.
[0045] FIG. 7 depicts typical agglomeration simulation result
showing particle clustering into a single portion of the original 1
.mu.m.sup.3 box.
[0046] FIG. 8 depicts simulations with uniform particle
distributions and different van der Waals force.
[0047] FIG. 9 depicts images of nanoparticle agglomeration for 4
different strong van der
[0048] Waals cases with particle size standard deviations of 5 nm
and 25 nm.
[0049] FIGS. 10A and 10B depict plots of nanoparticle agglomeration
(as void fraction) for 4 different strong van der Waals cases with
particle size standard deviations of 5 nm and 25 nm.
[0050] FIG. 11 depicts images of nanoparticle agglomeration for 4
different weak van der Waals cases with particle size standard
deviations of 5 nm and 25 nm.
[0051] FIGS. 12A and 12B depict plots of nanoparticle agglomeration
(as void fraction) for 4 different weak van der Waals cases with
particle size standard deviations of 5 nm and 25 nm.
[0052] FIG. 13 depicts images of nanoparticle agglomeration for 2
different no van der Waals cases with particle size standard
deviations of 5 nm and 25 nm.
[0053] FIGS. 14A and 14B depict plots of nanoparticle agglomeration
(as void fraction) for 4 different weak van der Waals cases with
particle size standard deviations of 5 nm and 25 nm.
[0054] FIGS. 15A and 15B depict images of agglomeration of about
100 nm diameter nanoparticles in powder form and images of about
100-nm diameter nanoparticles spread onto surface and dried.
[0055] FIGS. 16A, 16B, 16C, 16D show a plot of simulated electric
field phasor (FIG. 16C) and temperature profile (FIG. 16A) for
loosely packed particle bed with uniform particle distribution
showing good heat transfer into the bulk of the powder bed (FIG.
16D).
[0056] FIG. 17 shows a part that has been built using this
continuum modeling approach. This part was formed by scanning the
laser in a square pattern for each build layer.
[0057] FIG. 18 is a diagram of an exemplary micro-selective laser
sintering system in accordance with an illustrative embodiment.
[0058] FIGS. 19A and 19B are detailed diagrams of the exemplary
micro-selective laser sintering system of FIG. 18 in accordance
with an illustrative embodiment.
[0059] FIG. 20 depicts a diagram of a method of operating the
.mu.-SLS system in accordance with an illustrative embodiment.
[0060] FIG. 21 depicts non-exhaustive exemplary three-dimensional
parts that may be fabricated with the exemplified micro-SLS systems
and the methods.
[0061] FIG. 22 illustrates an exemplary computer that can be used
for predicting mechanical and electrical properties of parts
produced by selective laser sintering of powder beds.
DETAILED DESCRIPTION
[0062] The nanoparticle powder and nanoparticle ink described
herein may be understood more readily by reference to the following
detailed description of specific aspects of the disclosed subject
matter and the Examples included therein.
[0063] Before the present nanoparticle powder and nanoparticle ink
are disclosed and described, it is to be understood that the
aspects described below are not limited to specific synthetic
methods or specific reagents, as such may, of course, vary. It is
also to be understood that the terminology used herein is for the
purpose of describing particular aspects only and is not intended
to be limiting.
[0064] Also, throughout this specification, various publications
are referenced. The disclosures of these publications in their
entireties are hereby incorporated by reference into this
application in order to more fully describe the state of the art to
which the disclosed matter pertains. The references disclosed are
also individually and specifically incorporated by reference herein
for the material contained in them that is discussed in the
sentence in which the reference is relied upon.
[0065] General Definitions
[0066] In this specification and in the claims that follow,
reference will be made to a number of terms, which shall be defined
to have the following meanings.
[0067] Throughout the description and claims of this specification
the word "comprise" and other forms of the word, such as
"comprising" and "comprises," means including but not limited to,
and is not intended to exclude, for example, other additives,
components, integers, or steps.
[0068] As used in the description and the appended claims, the
singular forms "a," "an," and "the" include plural referents unless
the context clearly dictates otherwise. Thus, for example,
reference to "a composition" includes mixtures of two or more such
compositions, reference to "an agent" includes mixtures of two or
more such agents, reference to "the component" includes mixtures of
two or more such components, and the like.
[0069] "Optional" or "optionally" means that the subsequently
described event or circumstance can or cannot occur, and that the
description includes instances where the event or circumstance
occurs and instances where it does not.
[0070] Ranges can be expressed herein as from "about" one
particular value, and/or to "about" another particular value. By
"about" is meant within 5% of the value, e.g., within 4, 3, 2, or
1% of the value. When such a range is expressed, another aspect
includes from the one particular value and/or to the other
particular value. Similarly, when values are expressed as
approximations, by use of the antecedent "about," it will be
understood that the particular value forms another aspect. It will
be further understood that the endpoints of each of the ranges are
significant both in relation to the other endpoint, and
independently of the other endpoint.
[0071] It is understood that throughout this specification the
identifiers "first" and "second" are used solely to aid in
distinguishing the various components and steps of the disclosed
subject matter. The identifiers "first" and "second" are not
intended to imply any particular order, amount, preference, or
importance to the components or steps modified by these terms.
[0072] Nanoparticle Powder and Nanoparticle Ink
[0073] Disclosed herein are nanoparticle powder and nanoparticle
ink. As used herein, "nanoparticle" means any structure with one or
more nanosized features. A nanosized feature can be any feature
with at least one dimension less than 1 .mu.m in size. For example,
a nanosized feature can comprise a nanowire, nanotube,
nanoparticle, nanopore, and the like, or combinations thereof. As
such, the nanoparticle powder and nanoparticle ink can comprise,
for example, a nanowire, nanotube, nanoparticle, nanopore, or a
combination thereof.
[0074] In some examples, a plurality of nanoparticles of the
nanoparticle powder and nanoparticle ink can comprise a plurality
of metal particles. The plurality of metal particles can, for
example, comprise a metal selected from the group consisting of Au,
Ag, Pt, Pd, Cu, Al, Sn, Pb, Ni, Zn, and combinations thereof. In
some embodiments, the plurality of metal particles can comprise a
metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti,
V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh,
Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb,
Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and
combinations thereof.
[0075] The plurality of nanoparticles in the nanoparticle powder
and nanoparticle ink can have an average particle size. "Average
particle size," "mean particle size," and "median particle size"
are used interchangeably herein, and generally refer to the
statistical mean particle size of the particles in a population of
particles. For example, the average particle size for a plurality
of particles with a substantially spherical shape can comprise the
average diameter of the plurality of particles. For a particle with
a substantially spherical shape, the diameter of a particle can
refer, for example, to the hydrodynamic diameter. As used herein,
the hydrodynamic diameter of a particle can refer to the largest
linear distance between two points on the surface of the particle.
Mean particle size can be measured using methods known in the art,
such as evaluation by scanning electron microscopy, transmission
electron microscopy, and/or dynamic light scattering.
[0076] The plurality of nanoparticles in the nanoparticle powder
and nanoparticle ink can have, for example, an average particle
size of about (e.g., within.+-.0.5) 8 nanometers (nm), about 9 nm,
about 10 nm, about 11 nm, about 12 nm, about 13 nm, about 14 nm,
about 15 nm, about 16 nm, about 17 nm, about 18 nm, about 19 nm,
about 20 nm, about 21 nm, about 22 nm, about 23 nm, about 24 nm,
about 25 nm, about 26 nm, about 27 nm, about 28 nm, about 29 nm,
about 30 nm, about 31 nm, about 32 nm, about 33 nm, about 34 nm,
about 35 nm, about 36 nm, about 37 nm, about 38 nm, about 39 nm,
about 40 nm, about 41 nm, about 42 nm, about 43 nm, about 44 nm,
about 45 nm, about 46 nm, about 47 nm, about 48 nm, about 49 nm,
about 50 nm, about 51 nm, about 52 nm, about 53 nm, about 54 nm,
about 55 nm, about 56 nm, about 57 nm, about 58 nm, about 59 nm,
about 60 nm, about 61 nm, about 62 nm, about 63 nm, about 64 nm,
about 65 nm, about 66 nm, about 67 nm, about 68 nm, about 69 nm,
about 70 nm, about 71 nm, about 72 nm, about 73 nm, about 74 nm,
about 75 nm, about 76 nm, about 77 nm, about 78 nm, about 79 nm,
about 80 nm, about 81 nm, about 82 nm, about 83 nm, about 84 nm,
about 85 nm, about 86 nm, about 87 nm, about 88 nm, about 89 nm,
about 90 nm, about 91 nm, about 92 nm, about 93 nm, about 94 nm,
about 95 nm, about 96 nm, about 97 nm, about 98 nm, about 99 nm,
and about 100 nm.
[0077] In some embodiments, the average particle size can be 8
nanometers (nm) or more (e.g., 9 nm or more, 10 nm or more, 11 nm
or more, 12 nm or more, 13 nm or more, 14 nm or more, 15 nm or
more, 16 nm or more, 17 nm or more, 18 nm or more, 19 nm or more,
20 nm or more, 21 nm or more, 22 nm or more, 23 nm or more, 24 nm
or more, 25 nm or more, 26 nm or more, 27 nm or more, 28 nm or
more, 29 nm or more, 30 nm or more, 31 nm or more, 32 nm or more,
33 nm or more, 34 nm or more, 35 nm or more, 36 nm or more, 37 nm
or more, 38 nm or more, 39 nm or more, 40 nm or more, 45 nm or
more, 50 nm or more, 55 nm or more, 60 nm or more, 65 nm or more,
70 nm or more, or 75 nm or more). In some embodiments, the
plurality of nanoparticles of the nanoparticle powder and
nanoparticle ink can have an average particle size of 80 nm or less
(e.g., 75 nm or less, 70 nm or less, 65 nm or less, 60 nm or less,
55 nm or less, 50 nm or less, 45 nm or less, 40 nm or less, 39 nm
or less, 38 nm or less, 37 nm or less, 36 nm or less, 35 nm or
less, 34 nm or less, 33 nm or less, 32 nm or less, 31 nm or less,
30 nm or less, 29 nm or less, 28 nm or less, 27 nm or less, 26 nm
or less, 25 nm or less, 24 nm or less, 23 nm or less, 22 nm or
less, 21 nm or less, 20 nm or less, 19 nm or less, 18 nm or less,
17 nm or less, 16 nm or less, 15 nm or less, 14 nm or less, 13 nm
or less, 12 nm or less, 11 nm or less, 10 nm or less, or 9 nm or
less). The average particle size of the plurality of nanoparticles
of the nanoparticle powder and nanoparticle ink can range from any
of the minimum values described above to any of the maximum values
described above. For example, the plurality of nanoparticles of the
nanoparticle powder and nanoparticle ink can have an average
particle size of from 8 nm to 40 nm (e.g., from 8 nm to 40 nm, from
4 nm to 80 nm, from 8 nm to 20 nm, from 20 nm to 40 nm, from 40 nm
to 60 nm, from 60 nm to 80 nm, from 15 nm to 40 nm, or from 25 nm
to 35 nm).
[0078] In some examples, the plurality of nanoparticles in the
nanoparticle powder and nanoparticle ink can be substantially
monodisperse. "Monodisperse" and "homogeneous size distribution,"
as used herein, and generally describe a population of particles
where all of the particles are the same or nearly the same size. As
used herein, a monodisperse distribution refers to particle
distributions in which 80% of the distribution (e.g., 85% of the
distribution, 90% of the distribution, or 95% of the distribution)
lies within 25% of the median particle size (e.g., within 20% of
the median particle size, within 15% of the median particle size,
within 10% of the median particle size, or within 5% of the median
particle size).
[0079] The plurality of nanoparticles in the nanoparticle powder
and nanoparticle ink can comprise particles of any shape (e.g., a
sphere, a rod, a quadrilateral, an ellipse, a triangle, a polygon,
etc.). In some examples, the plurality of nanoparticles of the
nanoparticle powder and nanoparticle ink can have an isotropic
shape. In some examples, the plurality of nanoparticles of the
nanoparticle powder and nanoparticle ink can have an anisotropic
shape. In some examples, the plurality of nanoparticles of the
nanoparticle powder and nanoparticle ink are substantially
spherical.
[0080] Agglomeration and Powder Bed Formation in Microscale
Selective Laser Sintering Systems
[0081] Additive manufacturing (AM) has received a great deal of
attention for the ability produce three dimensional parts via laser
heating. One recently proposed method of making microscale AM parts
is through microscale selective laser sintering (.mu.-SLS) where
nanoparticles replace the traditional powders used in standard SLS
processes. However, there are many challenges to understanding the
physics of the process at nanoscale as well as with conducting
experiments at that scale; hence, modeling and computational
simulations are vital to understand the sintering process physics.
At the sub-micron (.mu.m) level, the interaction between
nanoparticles under high power laser heating raises additional
near-field thermal issues such as thermal diffusivity, effective
absorptivity, and extinction coefficients compared to larger
scales. Thus, nanoparticle's distribution behavior and
characteristic properties are very important to understanding the
thermal analysis of nanoparticles in a .mu.-SLS process.
[0082] Exemplified methods and system presents a discrete element
modeling (DEM) of how copper nanoparticles of a given particle size
distribution packs together in a .mu.-SLS powder bed. Initially,
nanoparticles are distributed randomly into the bed domain with a
random initial velocity vector and set boundary conditions. The
particles are then allowed to move in discrete time steps until
they reach a final steady state position, which creates the
particle packing within the powder bed. The particles are subject
to both gravitational and van der Waals forces since van der Waals
forces become important at the nanoscale. A set of simulations was
performed for different cases under both Gaussian and log-normal
particle size distributions with different standard deviations. The
results show that the van der Waals interactions between
nanoparticles has a great effect on both the size of the
agglomerates and how densely the nanoparticles pack together within
the agglomerates. In addition, exemplified methods and systems use
a method to overcome the agglomeration effects in .mu.-SLS powder
beds through the use of colloidal nanoparticle solutions that
minimize the van der Waals interactions between individual
nanoparticles.
[0083] Introduction
[0084] Harnessing heat transfer at the nanoscale is essential for
the development of microchips in semiconductors,
micro/nanoelectronics, integrated circuits, and micro/nano
electromechanical systems. Today, using nanomaterials such as
nanowires, carbon nanotubes, graphene, and metal nanoparticles is
common in these types of systems. Nanomaterials are generally used
in these systems because the thermal, optical, and
electromechanical properties of nanomaterials are quite different
from the properties of the bulk material and can be tuned by
controlling the shape and size of the nanostructure. The key fields
where nanomaterials have recently been used in additive
manufacturing technologies are microscale selective laser sintering
(.mu.-SLS), three-dimensional (3D) printing, and stereolithography.
.mu.-SLS is a relatively new additive manufacturing technique in
which the structures or objects are fabricated from the bottom up
by adding materials layer upon layer. In this technique, a laser
that has been focused down to approximately 1 .mu.m is used to
sinter together nanoparticles in a designed pattern on each layer
before the next layer of nanoparticles is added to the system. This
process is then repeated until an entire 3D structure with
microscale features is fabricated. Through the use of precise
focusing objectives, ultrafast lasers, and nanoparticle based
powder beds it is possible to achieve micron scale feature
resolutions with this technique.
[0085] .mu.-SLS has many advantages over other manufacturing
techniques in terms of the flexibility, cost, and finishing
quality. Furthermore, .mu.-SLS provides design freedom and has a
lower level of waste and harmful chemicals. Using nanoparticles
which can be synthesized with different shapes such as rods or
spheres for microscale selective laser sintering can also
significantly improve the sintering characteristics and the
finishing quality of the parts. However, models for nanoparticle
interactions and powder bed generation with nanoparticles are not
available for SLS at nanoscale. This is because nanoscale modeling
offers many challenges; for instance, a continuum model which is
used for micro and larger scales is no longer valid. Also, a ray
tracing model cannot be used to obtain the extinction and effective
absorption coefficient of a powder bed as the laser wavelength is
greater than the characteristic length of the particles. Hence,
modeling the nanoscale powder bed with nanoparticles for SLS is
quite different from modeling micro or larger scales. For example,
van der Waals forces, which are the sum of the attractive or
repulsive intermoleculer attractions between molecules, dominate
interactions between the particles at nanoscale. These van der
Waals interactions can create significant agglomeration effects in
particle beds containing nanoscale powders which are not typically
seen in SLS powder beds that contain only microscale powders. These
agglomeration effects can significantly reduce the packing density
of the particles in the powder bed which can result in significant
voids in the final sintered part. Additionally, particle size
distribution is another factor affecting the sintering process at
the submicron level. Most powder beds with nanoparticles have
non-uniform size distributions which effect the sintering quality
and overall shrinking of the parts produced. Hence, it is essential
to model the particle-particle interaction at nanoscale accurately
in order to understand the overall powder bed and size distribution
effect on the selective laser sintering process. Therefore, in
order to better understand the parameters that effect void
formation in .mu.-SLS parts, the exemplified methods and systems
use discrete element modeling techniques to investigate the role of
van der Waals forces and particle size distribution on the packing
density of nanoparticles in a .mu.-SLS powder bed.
[0086] Modeling Approach
[0087] The powder bed, consisting of solid, spherical nanoparticles
that are generated by defining a position and radius, is created
using the discrete element method (DEM) in a multiphase
computational fluid dynamics, MFIX. Particle packings are generated
using the MFIX-DEM discrete mass inlet function with each particle
interacting with its neighboring particles. The particles are
initially distributed randomly within the powder bed domain and are
given an initial velocity and an initial set of boundary
conditions. Forces such as gravitational and van der Waals forces
are also applied to each particle. Material properties such as
diameter, density, and different particle size distribution can
also be defined by the user. The MFIX-DEM approach is explained in
detail in R. Garg, J. Galvin, T. Li, and S. Pannala, 2012,
"Documentation of open-source MFIX-DEM software for gas-solids
flows," which is incorporated by reference herein in its entirety,
and summarized briefly below. The exemplified simulation analysis
predicts different force analysis contributions such as van der
Waals and gravitational force within given particle
distributions.
[0088] 2.1 Discrete Element Method (DEM)
[0089] In the discrete element method (DEM), a number of spherical
particles, N.sub.m, with diameter, D.sub.m, and density,
.rho..sub.sm are used to represent the nanoparticle in the powder
bed. The total number of particles in the powder bed is given by
the summation of each spherical particle over the total number of
solid phases, M, as given by equation (1).
N=.SIGMA..sub.m=1.sup.MN.sub.m Equation (1)
[0090] Each of the N particles is defined within a Lagrangian
reference at time t by its position, X.sup.(i) (t), linear
velocity, V.sup.(i)(t), angular velocity, .omega..sup.(i)(t),
diameter, D.sup.(i), density .rho..sup.(i), and mass m.sup.(i). The
position, linear velocity and angular velocities of the
i.sup.thparticle change with time according to Newton's laws as
below:
dX ( i ) ( t ) dt = V ( i ) ( t ) Equation ( 2 ) m ( i ) dV ( i ) (
t ) dt = F T ( i ) = m ( i ) g + F d ( i ) ( t ) + F c ( i ) ( t )
Equation ( 3 ) I ( i ) d .omega. ( i ) ( t ) dt = T ( i ) Equation
( 4 ) ##EQU00007##
[0091] The total drag force, F.sub.d(i), is found by the summation
of pressure and viscous forces. The net contact force, F.sub.c (i),
is the force acting on the particle as a result of contact with
other particles and the total force on each particle,
F.sub.T.sup.(i), is found through the summation of all forces
acting on the i.sup.thparticle. Also, the summation of all torques
acting on the i.sup.th particle is represented by T.sup.(i).
[0092] 2.1.1 Contact Forces
[0093] A spring-dashpot model, based on a soft-sphere model of the
particles, is used herein for the particle interactions modeling.
This model also accounts for the degree of overlapping between two
nanoparticles as it imposes no restrictions for multi-particle
contacts.
[0094] FIG. 1 depicts a schematic of two particles in contact. For
the soft-sphere collision shown in FIG. 1, two particles, i and j,
in contact have diameters equal to D.sup.(i) and D.sup.(j), and are
located at positions X.sup.(i) and X.sup.(j) move with linear
velocity, V, and an angular velocity, .omega.. The normal overlap
between the particles is given by equation (5) and the unit vector
along the line of contact between each particle is given by
equation (6).
.delta. n = 0.5 ( D ( i ) + D ( j ) ) - X ( i ) + X ( j ) Equation
( 5 ) .eta. ij = ( D ( i ) + D ( j ) ) X ( i ) + X ( j ) Equation (
6 ) ##EQU00008##
[0095] The relative velocity of the point of contact is given by
equation (7) where L.sup.(i) and L.sup.(j) are the distance to the
contact point from the center of each particle.
V.sub.ij=V.sup.(i)-V.sup.(j)+(L.sup.(i).omega..sup.(i)+L.sup.(j).omega..-
sup.(j)).times..eta..sub.ij Equation (7)
[0096] FIG. 2 depicts a schematic of the Spring-dashpot system. For
the soft-sphere model used in this exemplified methods and systems,
the overlap between two adjacent particles is represented by a
system of springs and dashpots. The springs are used to model
elastic interactions between the particles and the dashpots
represent the kinetic energy loss due to inelastic collisions. The
springs are given stiffness's in both the normal, k.sub.n, and
tangential, k.sub.t, directions. These stiffness are dependent on
the elastic modulus of the nanoparticles that are interacting.
Likewise, the dashpot damping coefficients given to each particle
interaction in the normal, .eta..sub.n, and tangential,
.eta..sub.t, directions is determined by the inelastic scattering
losses of each nanoparticle collision. Therefore, the normal and
tangential components of the contact force, F.sub.ij, at time t,
can be decomposed into the spring force, F.sub.ij.sup.S and the
dashpot force, F.sub.i,j.sup.D, as given by equations (8) and
(9).
F.sub.nij(t)=F.sub.nij.sup.S(t)+F.sub.nij.sup.D(t) Equation (8)
F.sub.tij(t)=F.sub.tij.sup.S(t)+F.sub.tij.sup.D(t) Equation (9)
[0097] The normal spring force, F.sub.nij.sup.S, at any time during
the contact between two nanoparticles can be calculated using
Hooke's law with the displacement equal to the overlap, S.sub.n,
between the particles as shown in equation (10).
F.sub.nij.sup.S=-k.sub.n.delta..sub.n.eta..sub.ij Equation (10)
[0098] Similarly, at any time during the contact, the tangential
spring force is given by equation (11) where .delta..sub.t is the
tangential displacement. The tangential displacement at the start
of the contact can be calculated as using equation (12).
F tij S = - k t .delta. t Equation ( 11 ) .delta. t = V tij min (
.delta. n V ij .eta. ij , .DELTA. t ) Equation ( 12 )
##EQU00009##
[0099] 2.1.2 Hertzian Model
[0100] The linear spring-dashpot model described in the previous
section only works well for small overlap between nanoparticles.
For larger overlaps, the linear model must be replaced by a
Hertzian contact model. The Hertzian contact model is described in
H.Hertz, "Uber die beruhrung fester elastischer korper" (i.e., "On
the Contact of Elastic Solids"), J reine and angewandte Mathematik
1882; 94:156-71.
[0101] In the Hertzian contact model, the normal and tangential
effective spring stiffnesses between two particles in contact can
be calculated using the elastic modulus and Poisson's ratio of the
nanoparticles as shown in equations (13) and (14) where E.sub.mand
E.sub.l are the elastic moduli and .sigma..sub.m and .sigma..sub.l
are the Poisson ratios for the m.sup.th and l.sup.th nanoparticles.
In addition, G.sub.m, and G.sub.l are the shear moduli of each
nanoparticle as calculated by equations (15) and (16), and r.sub.ml
is the effective contact radius as given by equation (17).
.delta. n , ij = 4 3 E m E l r ml E m ( 1 - .sigma. l 2 ) + E l ( 1
- .sigma. m 2 ) .delta. n , ij 1 / 2 Equation ( 13 ) k t , ij = 16
3 G m G l r ml G m ( 2 - .sigma. l ) + G l ( 2 - .sigma. m 2 )
.delta. n , ij 1 / 2 Equation ( 14 ) G m = E m 2 ( 1 + .sigma. m )
Equation ( 15 ) G l = E l 2 ( 1 + .sigma. l ) Equation ( 16 ) 1 r
ml = 1 r ( m ) + 1 r ( l ) Equation ( 17 ) ##EQU00010##
[0102] 2.1.3 Relationship between Dashpot Coefficients and
Coefficients of Restitution
[0103] The relationship of normal dashpot coefficient .eta..sub.nml
and normal coefficient of restitution is given by equation (18)
where the effective mass (m.sub.eff) and collision time
(t.sub.nml.sup.col) between m.sup.th and n.sup.th solid-phases are
defined as
m eff = ( m m m l m m + m l ) and t nml col = .pi. ( k nml m eff -
n nml 2 4 m eff 2 ) - 1 / 2 . ##EQU00011##
.eta. mnl = m eff k nml 2 ln e nml .pi. 2 + ln e nml 2 Equation (
18 ) ##EQU00012##
[0104] Time step .DELTA.t is taken to be one fiftieth of the
minimum collision time (i.e. .DELTA.t=min(t.sub.col,ml/50)). The
normal spring stiffness coefficient is chosen to be .about.10.sup.5
N/m in order to prevent the time step problems due to the
complicated definition of spring coefficients in the simulation. By
following the Silbert et al. approach (described in Silbert et al.,
"Granular flow down an inclined plane: Bagnold scaling and
rheology," Phys. Rev. E 64, 051302, 2001, which is incorporated
herein in its entirety), the relationship of the tangential spring
stiffness coefficient (k.sub.tml) and the normal stiffness
coefficient (k.sub.n) is defined as
k tml = 2 5 k nml . ##EQU00013##
The tangential damping coefficient and the normal damping
coefficient is given as
.eta. tml = 1 2 n nml . ##EQU00014##
Hence, tne coefficient of normal restitution matrix and the
tangential coefficient of restitution are written as M.times.M
symmetric matrices for M solid-phases shown in equation (19). As
the matrix is symmetric, the top diagonal or lower diagonal values
(M(M-1)/2) for normal coefficient of restitution between the
particle interactions are set to define the matrix.
[ e n ] = [ e n 11 e n 12 e n 1 M e nM 1 e nM 2 e nMM ] Equation (
19 ) ##EQU00015##
[0105] 2.1.4 Van Der Waals Forces
[0106] At the nanoscale, van der Waals forces become the dominant
force and play an important role on particle interaction. Moreover,
the van der Waals force becomes very significant at a very short
distance and can cause the agglomeration of nanoparticles. Various
van der Waals force models that predict the interactions between
two nanospherical particles have been suggested (for example, Li et
al. "London-van der Waals adhesiveness of rough particles," Powder
Technology 161, 248-255 (2006)). However, the initial van der Waals
models did not consider surface roughness, which plays a key role
in the adhesion of nanoparticles. In fact, no real surface is
smooth at the submicron level; even polished silicon wafers are
rough at sub-nanometer scale. Hence, the adhesion of nanoparticles
is of significant importance in nanoscale applications such as
semiconductor fabrication and drug delivery. Recently more complex
models have been used to explain the sphere-sphere van der Waals
interaction by including an asperity value which depends on surface
roughness. Hence, understanding both the roughness and asperity of
the surfaces at nanoscale is crucial for modeling the van der Waals
forces accurately and thus for modeling powder bed formation in
microscale selective laser sintering.
[0107] The van der Waals force interaction between two
nanoparticles or between particle and a surface (i.e., the wall of
the simulation box) are calculated using the inner and outer cutoff
values of the particle or the wall as given in equation (20) and
(21) where A is the Hamaker constant, R is the equivalent radius, r
is the separation distance, .phi. is the surface energy, D is the
particle diameter, rP.sub.inner cutoff and rP.sub.outer cutoff are
the inner and outer cutoff van der Waals value between
particle-particle interaction, and asperity, h, is the general
definition of roughness and impurity on the surface. rW.sub.inner
cutoff and rW.sub.outer cutoff are the inner and outer cutoff value
between particle-wall interaction.
F = AR 12 r 2 ( ( Asperities Asperities + R ) + 1 ( 1 + Asperities
r ) 2 ) Equation ( 20 ) F = 2 .pi. .PHI. R ( ( Asperities
Asperities + R ) + 1 ( 1 + Asperities r inner cutoff ) 2 ) Equation
( 21 ) .PHI. = A 24 .pi. r inner cutoff 2 Equation ( 22 )
##EQU00016##
[0108] FIG. 3 depicts a schematic view of nanoparticles in the
domain. The figure illustrates the followings: r is the particle's
distance, h is the asperity or surface roughness, w is the
separation distance between wall and the particle, L.sub.w and
L.sub.p are the distance parameters used for surface-adhesion
cohesion. Typical simulation parameters for each simulation run are
given in Table 1.
TABLE-US-00001 TABLE 1 Parameter Value Minimum Particle Radius 40
nm Maximum Particle Radius 500 nm Surface Asperity Size 5 nm Wall
Inner Cutoff Value 1 .mu.m Wall Outer Cutoff Value 5 .mu.m
Particle-to-Particle Spring Constant 10.sup.8 N/m Particle-to-Wall
Spring Constant 10.sup.9 N/m
[0109] 2.1.5 Particle--Particle and Particle--Wall Interaction
[0110] For the nanoparticle-to-nanoparticle interactions, if the
inner cutoff radius plus the radii of the two particles is less
than the distance parameter, L.sub.P, then the van der Waals
interaction is calculated using equation 21. However, if the
L.sub.P is greater than this value but less than the outer cutoff
radius plus the radii of the two nanoparticles then equation 20 is
used to calculate the van der Waals interaction. If the distance
between the two particles is greater than outer cutoff distance
than the van der Waals interaction between the two particles is
assumed to be negligible.
[0111] Similarly, for wall-nanoparticle interactions, if the inner
cutoff radius plus the diameter of the nanoparticle is less than
L.sub.P then the van der Waals interaction between the particle and
the wall is calculated using equation 21. However, if the L.sub.P
is greater than this value but less than the outer cutoff radius
plus the diameter of the nanoparticle then equation 20 is used to
calculate the van der Waals interaction. If the distance between
the wall and the particle is greater than outer cutoff distance
then the van der Waals interaction between the two particles is
assumed to be negligible.
[0112] 2.2 Nanoparticle Size Distribution
[0113] Particle-size distribution within the powder bed can
significantly affect the mechanical and thermal characteristics of
the powder bed such as the surface plasmon resonances and
excitation enhancement which can significantly change the quality
of the process and the overall level of part shrinkage. Most
nanoparticle powder beds have a non-uniform particle size
distribution since it is almost impossible to obtain a uniform,
mono-sized nanoparticle powder bed. Particle size distributions
have been analyzed to understand the effect different distribution
characteristics such as narrow, broad size and finer,
poly-dispersed structures can have on how well particles pack
together. The particle size distributions used herein are explained
at the following section.
[0114] 2.2.1 Gaussian Distribution
[0115] FIG. 4 depicts a schematic of typical Gaussian distribution.
Gaussian distribution is a very useful probability method
especially when the number of random variables is very large. The
probability density of the Gaussian distribution is given in
equation (23) where .mu. is the mean or median and .theta. is the
standard deviation of the distribution. The variance can also be
defined as .theta..sup.2. The Gaussian distribution is non-zero
over the region and is symmetric about its median.
P ( x ) = 1 .sigma. 2 .pi. ( e - ( x - .mu. ) 2 2 .sigma. 2 )
Equation ( 23 ) ##EQU00017##
[0116] The distribution is properly normalized as
f.sub.-.infin..sup.+.infin.P(x)dx=1. The cumulative distribution,
D(x), function can also be defined as in equation(y) where erf is
the so-called error function.
D ( x ) = .intg. - .infin. + .infin. P ( x ' ) dx ' = 1 .sigma. 2
.pi. ( e - ( x ' - .mu. ) 2 2 .sigma. 2 ) dx ' = 1 2 [ 1 + erf ( x
- .mu. .sigma. 2 ) ] Equation ( 24 ) ##EQU00018##
[0117] 2.2.2 Log-Normal Distribution
[0118] FIG. 5 depicts a schematic of typical log-normal
distribution. Log-normal distribution is a continuous distribution
whose logarithm has a normal distribution. It is a very common
model used in the fields where the boundaries and the threshold of
the distribution is estimated or known. Also, it is applied to
model continuous random quantities when the distribution is skewed.
For example a nanoparticle distribution that has a hard minimum
size cutoff at 0 nm but can have some very large particles could be
well modeled using the log-normal distribution. The log-normal
distribution is given in equation (26) where x .di-elect cons. (0,
.infin.). Also, .mu. and .sigma. are called the location and the
scale parameter, respectively. These parameters can be related with
the mean (.mu.), standard deviation (.sigma.), and variance (v) of
the non-logarithmic values given as in equation (25). Also, mean
and the median of the distribution can be defined as exp
( .mu. + .sigma. 2 2 ) ##EQU00019##
and exp(.mu.), respectively.
.mu. = ln ( m 1 + v m 2 ) , .sigma. = ln ( 1 + v m 2 ) Equation (
25 ) P ( x ) = 1 2 .pi. .sigma. x exp ( - [ ln ( x ) - .mu. ] 2 2
.sigma. 2 ) Equation ( 26 ) ##EQU00020##
[0119] The cumulative distribution, D(x), function can also be
defined as in equation (27) where erf is the error function.
D ( x ) = .intg. - .infin. + .infin. P ( x ' ) dx ' = 1 2 .pi.
.sigma. x ' exp ( - [ ln ( x ' ) - .mu. ] 2 2 .sigma. 2 ) dx ' = 1
2 [ 1 + erf ( ln ( x ) - .mu. 2 .sigma. ) ] Equation ( 27 )
##EQU00021##
[0120] 2.2 Computational Details of Particle Bed Formation
[0121] In the particle bed formation algorithm within the MFIX-DEM
framework, a nanoparticle with a random size, linear velocity, and
angular velocity is initially placed at a random position within a
1 .mu.m.sup.3 box. Another nanoparticle is then placed within the
box at a random position with the constraint that the particles do
not initially overlap. This process continues until no additional
particles can be placed within the box without overlapping with the
particles already in the box. This results in a 1 .mu.m.sup.3, 3-D
box that is full of nanoparticles each with a randomly assigned
size, position and initial linear and angular velocities. The 1
.mu.m.sup.3 box is also organized such that the only particle-wall
interactions that occur happen at the bottom of the box. In other
words, there is no interaction between the particle-wall at the
sides and the top surfaces of the box. The size of the particles in
the box is determined by randomly selecting the size of each
particle using a particle size distribution function. Three
different distribution functions were used herein: (1) a uniform
distribution, (2) a Gaussian distribution, and (3) a log-normal
distribution.
[0122] Once the initial particle sizes, positions, velocities and
boundary conditions are set, a time step is given to the system and
the particles are allowed to move and interact. After the time
step, the new position of each particle can be calculated and the
interactions between particles can be determined from the overlap
between particles. These overlap values determine the forces on
each nanoparticle and the amount of energy dissipated by each
particle in the time step period. A new set of particle positions,
velocities, and boundary conditions can then be determined for the
next time step. This process is repeated until the particles reach
a steady configuration within the powder bed.
[0123] 2.2.1 Time Integration
[0124] A first-order time integration scheme is used to determine
the position and the velocity of each particle at each time step.
In this scheme, the translational velocity, particle center
position, and the angular velocity at time t+.DELTA.t are obtained
from values at time t using equations (28), (29), and (30) where
F.sub.T.sup.(i) and T.sup.(i) are the total force and torque acting
on the particle.
V ( i ) ( t + .DELTA. t ) = V ( i ) ( t ) + F T ( i ) ( t ) m ( i )
.DELTA. t Equation ( 28 ) X ( i ) ( t + .DELTA. t ) = X ( i ) + V (
i ) ( t + .DELTA. t ) .DELTA. t Equation ( 29 ) .omega. ( i ) ( t +
.DELTA. t ) = .omega. ( i ) ( t ) + T ( i ) ( t ) I ( i ) .DELTA. t
Equation ( 30 ) ##EQU00022##
[0125] 2.2.2 Neighbor Search Algorithm
[0126] FIG. 6 depicts the neighbor search algorithm for
"cell-linked list" in 2D scheme. The neighbor search algorithm is
one of the most important and time consuming components of any
particle--based simulation. Each particle is marked according to
the cell in which the center of the particle is located and a
"cell--linked list" search algorithm is used to find the particles
neighbors. In this algorithm, the simulation is broken down into
smaller boxes and only particles within the same box as the
particle being investigated or in neighboring boxes are considered.
For example, as shown by the 2-D schematic in FIG. 6, if the
particle of interest is the one represented by the filled circle,
then the particles belonging to the 9 (27 for the 3-D case)
adjacent cells, along with particles belonging to the same cell as
the particle of interest, are considered as potential neighbors.
Thus, only these particles are further checked against the particle
of interest for a neighbor contact. By eliminating most of the
particles in the box from the search algorithm, the total
simulation time is significantly reduced. In this search algorithm,
any two particles i and j that are located at X(.sup.i) and
X.sup.(j), and have radii R.sub.i and R.sub.j, are considered
neighbors if they satisfy the following condition in equation (31)
where K is an interaction distance constant.
|X.sup.(i)-X.sup.(j)|<K(R.sub.i+R.sub.j) Equation (31)
[0127] This search algorithm can, therefore, be used to determine
which particles are touching or overlapping as neighbors. This
neighbor search algorithm is run for each time step in order to
ensure that the simulation does not miss any possible collision
between the particles.
[0128] 2.3 van der Waals Interactions
[0129] Agglomeration of nanoparticles is driven by van der Waals
interactions between nanoparticles or between a nanoparticle and a
surface. For the agglomeration simulations, three general types of
van der Waals interactions are considered: (1) a strong van der
Waals interaction case where two dry copper particles interact with
each other, (2) a weak van der Waals interaction case where the
copper nanoparticles are assumed to be incased in a thin polymer or
oxide coating, and (3) a no van der Waals interaction case where
the particles are assumed to be in a perfect colloidal solution.
The strength of the van der Waals interactions in each case set by
adjusting the Haymaker constant of the nanoparticle interaction. In
this model, there are assumed to be no van der Waals interactions
between the top of box and the nanoparticles since in the top layer
of the powder bed is open to the environment. Similarly, there are
assumed to be no van der Waals forces between the sides of the box
and the nanoparticles since each box is a discrete element within
the continuous powder bed so particles may travel through these
boundaries on the side walls. However, there is assumed to be a van
der Waals interaction between the nanoparticles and the bottom
surface of the box since the bottom surface will contain the
nanoparticles from the previous sintered layer. The Hamaker
constants for each of the van der Waals interaction case [12] are
given in Table 2.
TABLE-US-00002 TABLE 2 Hamaker Constants for Various Types of van
der Waals Interactions Particle to Particle to Particle Bottom Wall
Hamaker Hamaker VDW Interaction Case Constant Constant Strong van
der Waals Interaction 28.4*10.sup.-20 J 14*10.sup.-20 J Weak van
der Waals Interaction 10*10.sup.-20 J 14*10.sup.-20 J No van der
Waals Interaction 0 J 14*10.sup.-20 J
[0130] 2.4 Particle Size Distributions
[0131] Herein, three different types of particle size distributions
were examined: (1) a uniform distribution where all the particles
were 100 nm in diameter, (2) a Gaussian distribution with a mean
diameter of 100 nm, and (3) a log-normal distribution with a mean
diameter of 100 nm. In addition, the Gaussian and log-normal cases
were tested with distribution standard deviations of 5 nm, 15 nm,
and 25 nm. Limits of 1 nm and 200 nm on the minimum and maximum
particle size respectively were also set for both the Gaussian and
log-normal distributions. The total number of the particles
generated in the 1 .mu.m3 simulation box for both the Gaussian and
log-normal distributions ranged from 263 particles of the 25 nm
standard deviation case to 455 for the 5 nm standard deviation
case.
[0132] 2.5 Void Fraction Analysis
[0133] FIG. 7 depicts typical agglomeration simulation result
showing particle clustering into a single portion of the original 1
.mu.m.sup.3 box.
[0134] Void fraction is defined as the volume of empty space
divided by the volume of space filled by nanoparticles in the
powder bed. Void fraction is an important parameter in determining
how well particles will sinter together in a selective laser
sintering process and in determining the quality of the final part
produced. Herein, the void fraction was calculated using two
different methods. In the first method (referred to herein as
method 1), the void fraction is found by considering the highest
and lowest particles' positions in the x, y, and z-axis and then
creating a box that bounds these particles. These new box bounds
are then used to determine the maximum volume that the particles
could fill (Vcube). This method provides a much better analysis
than considering the volume of the whole 1 .mu.m3 box since the
particles will always settle into some subsection of the original
box. Once the volume of the bounding box has been found, the void
fraction can be found by calculating the volume of all n number of
particles in the box and subtracting that volume from the box
volume and dividing by the void fraction as shown in equations (32)
through (34).
Fraction = Empty Fill Equation ( 32 Empty = V cube - j = 1 n 4 3
.pi. r j 3 Equation ( 33 ) V cube = ( ( max ( Position x + Diameter
2 ) - min ( Position x - Diameter 2 ) * ( max ( Position y +
Diameter 2 ) - min ( Position y - Diameter 2 ) * ( max ( Position z
+ Diameter 2 ) - min ( Position z - Diameter 2 ) ) Equation ( 34 )
##EQU00023##
[0135] The second method (referred to herein as method 2) for
calculating the void fraction is very similar to the first except
that only the change in the height of the agglomerated cluster in
the vertical direction is considered when calculating the bounding
box. The extent of the bounding box in the two horizontal
directions is set to be the width of the original 1 .mu.m.sup.3
box. This calculation allows us to take into account the effect
that clustering of nanoparticles into discrete agglomerates might
have on the overall packing density of the nanoparticles in the
powder bed. By comparing the void fraction results from each of the
two methods it is possible to separate out voids that are created
by the packing of the nanoparticles within an agglomerate and the
voids that are formed by the agglomeration process itself.
[0136] 2.6 Test Cases
[0137] The objective herein is to quantify and compare the
aggregation kinetics and colloidal stability of nanoparticle powder
beds with different types of inter-particle interaction forces. In
order to pursue that goal, simulations were performed as listed in
Table 3.
TABLE-US-00003 TABLE 3 Performed Simulation Data with Particle Size
Standard Deviations for Each Case in Nanometers Uniform Gaussian
Log-Normal Simulation Type Distribution Distribution Distribution
No van der Waals Std: NA Std: 25,15,5 Std: 25,15,5 Only Weak van
der Waals Std: NA Std: 25,15,5 Std: 25,15,5 Only Strong van der
Waals Std: NA Std: 25,15,5 Std: 25,15,5 Weak van der Waals with
Std: NA Std: 25,15,5 Std: 25,15,5 gravitational Strong van der
Waals with Std: NA Std: 25,15,5 Std: 25,15,5 gravitational
[0138] Results and Discussion--Uniform Distribution of
Particles
[0139] FIG. 8 depicts simulations with uniform particle
distributions and different van der Waals force. Overall, herein,
the uniform distribution of particles will be used as a basis of
comparison for evaluating the effect of particle size distribution
on the packing quality of the nanoparticles in the .mu.-SLS powder
bed. As can clearly be seen in FIG. 8, van der Waals forces play a
significant role in the agglomeration of particles at the
nanoscale. When the only forces applied to the nanoparticle system
are gravitational forces, then the particles are able to find their
lowest energy state and pack into an ordered cell. However, when
van der Waals forces are present individual particles adhere
together before they can reach their lowest energy state which
reduces the packing order. For example, when only gravitational
forces are applied to the system the void fraction is approximately
50%. However, when both van der Waals and gravitational forces are
applied to the system then the void fraction climbs to
approximately 65% due to the agglomeration effects created by the
van der Waals forces. Interestingly, when only van der Waals force
are considered in the absence of a gravitational driving force, the
void fraction is approximately 60%. This reduction in the void
fraction in the absence of the gravitational force may be due to
the fact the particles take a much longer time to settle into their
final positions if there is no global external driving force
pushing them towards their final resting position. Therefore, the
particle systems without the gravitational force may be able to
find a lower energy configuration and better packing than the
systems driven by gravitational forces.
[0140] Strong van der Waals Interaction Force Case
[0141] FIG. 9 depicts images of nanoparticle agglomeration for 4
different strong van der Waals cases with particle size standard
deviations of 5 nm and 25 nm.
[0142] The effect of particle size distribution on the packing
density for a pure copper nanoparticle system can be examined using
the strong van der Waals force interaction cases. In these types of
systems, the smallest particles in the system have the largest van
der Waals forces on them and, therefore, act as nucleation sites
for the formation of agglomerates. In general, the particle
distributions with the larger standard deviations pack better
(lower void fraction) than the distributions with the smaller
standard deviations; however, this is not a strong effect and it
can be overwhelmed by random variances do the randomized initial
conditions placed on the nanoparticles at the start of the
simulation. This general effect can be explained by the fact that
with the large particle size standard deviations, there are both
more very large and very small nanoparticles that all get packed
together. Therefore, the small nanoparticles can generally fill
into interstitial spaces between the larger particles in order to
increase the overall packing density of the system.
[0143] The exception to this trend is the completely uniform
distribution which agglomerates in a different way than the
distributions with some non-zero standard deviation. In even
distributions with the narrowest standard deviations, there are
occasionally small particles that can act like a nucleation site to
for agglomeration which results in a heterogeneous type nucleation
of the agglomerate. However, in the uniform distribution, there are
no small particles to act as a preferential nucleation site. This
results in homogeneous nucleation of the agglomerate in the uniform
distribution case. As a result of this homogeneous nucleation, the
uniform distribution tends to have a better packing density than
either the small standard deviation Gaussian or log-normal
distribution cases. This indicates that it may be the smallest
particles in the powder distribution that most effect agglomeration
and not the overall uniformity or size distribution of the
nanoparticles. Therefore, one strategy to reduce agglomeration
would be to eliminate all of the very small particles from the
powder bed. However, in practice it may be impossible to create
particle distributions without any small particles that can act as
nucleation sites. Overall, the results of these simulations show
that it is important to be able to measure and evaluate the size
distributions of the nanoparticles in a .mu.-SLS powder bed in
order to evaluate the effect these nucleation sites will have on
void formation.
[0144] FIGS. 10A and 10B depict plots of nanoparticle agglomeration
(as void fraction) for 4 different strong van der Waals cases with
particle size standard deviations of 5 nm and 25 nm. In FIG. 10A,
the void fractions are calculated based on particle's x,y and z
direction, i.e., method 1. In FIG. 10B, the based on particle's y
direction only (x=z=1 .mu.m), i.e., method 2. As can be seen in
FIGS. 10A and 10B, the void fraction calculated using method 1 is
always smaller than or equal to the void fraction calculated using
method 2 where the entire width of the initial bounding box is
considered in the calculation. This makes sense because the
horizontal extent of the nanoparticles will always be smaller than
or equal to the original 1 .mu.m.sup.3 bounding box. Therefore, the
ratio of these two void calculation methods can be used as a proxy
for the extent of agglomeration in the nanoparticle system and can
be used to separate the effect of packing voids from voids caused
by agglomeration.
[0145] Results and Discussion--Weak van der Waals Interaction
Case
[0146] FIG. 11 depicts images of nanoparticle agglomeration for 4
different weak van der Waals cases with particle size standard
deviations of 5 nm and 25 nm.
[0147] FIGS. 12A and 12B depicts plots of nanoparticle
agglomeration (as void fraction) for 4 different weak van der Waals
cases with particle size standard deviations of 5 nm and 25 nm. In
FIG. 12A, the void fractions are calculated based on particle's x,y
and z direction, i.e., method 1. In FIG. 12B, the based on
particle's y direction only (x=z=1 .mu.m), i.e., method 2.
[0148] van der Waals interactions between nanoparticles can be
reduced by coating the copper nanoparticles with a thin oxide or
polymer coating. This reduction in the van der Waals forces means
that only the very smallest nanoparticles produce a high enough
adhesion force to act as nucleation sites for agglomeration.
Therefore, there are fewer nucleation sties in the weak van der
Waals case than there were in the strong van der Waals case.
Because of these fewer number of nucleation sites, the
nanoparticles tend to agglomerate into columnar-like crystals as
can be clearly seen for the Gaussian, weak van der Waals force case
(2b) with a particle size standard deviation of 5 nm as shown in
FIG. 11. This produces a relatively efficient packing of the
particles within the agglomerate (similar to the strong van der
Waals case) but does increase the overall agglomerate size. Without
wishing to be bound to a particular theory, this is because the
lower number of nucleation sites in the weak van der Waals case
cause the agglomerate to generally form from a single nucleation
site in the simulation instead of multiple nucleation sites as is
the case with the strong van der Waals case. This result can be
seen when the void fraction is calculated using method 2. Overall,
when the void fractions are calculated for the weak van der Waals
case using method 1 they are not significantly different from the
void fractions calculated in the strong van der Waals case.
However, when the void fractions are calculated using method 2, the
week van der Waals cases produce void fractions that are about 10%
larger than those that were produced in strong van der Waals case.
This suggests that just reducing the van der Waals interactions
between the nanoparticles alone may not be enough to reduce
agglomeration in .mu.-SLS powder beds.
[0149] Results and Discussion--No van der Waals (Gravitational
Only) Case
[0150] FIG. 13 depicts images of nanoparticle agglomeration for 2
different no van der Waals cases with particle size standard
deviations of 5 nm and 25 nm.
[0151] FIGS. 14A and 14B depict plots of nanoparticle agglomeration
(as void fraction) for 4 different weak van der Waals cases with
particle size standard deviations of 5 nm and 25 nm. In FIG. 14A,
the void fractions are calculated based on particle's x,y and z
direction, i.e., method 1. In FIG. 14B, the based on particle's y
direction only (x=z=1 .mu.m), i.e., method 2.
[0152] One potential method to reduce agglomeration in .mu.-SLS
powder beds is to dispense the powder in a liquid as a colloidal
solution and then to coat the solution into a uniform layer. This
layer can then be allowed to dry in order to produce the new
.mu.-SLS powder bed layer. The advantage of this method is that
while the particles are in the colloidal solution, surfactants can
be used to effectively eliminate van der Waals interactions between
the particles. The simulation results indicate that the presence of
van der Waals interactions within the powder bed can cause the void
fraction in the particle agglomerates to increase by up to 34% for
the low standard deviation, Gaussian case and by up to 40% in the
low standard deviation, log-normal distribution case.
[0153] In addition, the elimination of the van der Waals
interactions eliminates the large scale formation of agglomeration
within the .mu.-SLS powder bed. This can be seen by the fact that
when the void density is calculated using each of the two methods
presented, both methods produce the exact same results. Therefore,
the two bar charts created using each of the two void fraction
calculation methods in FIGS. 14A and 14B are identical. This
indicates that the particles are spreading out to the edges of the
initial bounding box, as can be seen in FIG. 13, so that they can
form continuous nanoparticle layers. Therefore, one of the key to
producing good, uniform sintering layers in .mu.-SLS powder beds is
to eliminate the van der Waals interactions between the
nanoparticles in the powder beds.
[0154] Comparison to Experimental Results
[0155] FIGS. 15A and 15B depict images of agglomeration of about
100 nm diameter nanoparticles in powder form and images of about
100-nm diameter nanoparticles spread onto surface and dried.
[0156] To validate the predictions made by the simulations
presented in the previous section, several nanoparticle surface
spreading experiments were performed. First, 100 nm diameter
average size copper nanoparticles from various commercial venders
(US Research Nano and MK Impex) were spread onto glass slides and
silicon substrates. As shown in FIG. 15A, these nanoparticles
tended to agglomerate into very large, discrete assemblies. These
agglomerated particles assemblies can be on the order of 100 .mu.m
in diameter and can consist of hundreds of thousands of
nanoparticles. These agglomerates contain many more particles than
it is possible to simulate using the discrete element method, but
the results from the DEM simulations do show very similar
agglomeration formation within the smaller simulation volume for
both the strong and weak van der Waals cases. In addition, samples
passivated with oxide, carbon, and polymer coatings were tested to
see how much agglomeration takes place in powder beds generated
using these types of passivated particles. The passivation coatings
are meant of reduce agglomeration the nanoparticles when they are
in powder form by reducing the van der Waals interactions between
the particles. However, even with the passivated coatings,
significant agglomeration of the nanoparticles was observed. This
observed result matches very well what the discrete element model
simulations for the weak van der Waals case predict. This indicates
that the simulations that include non-zero van der Waals
interactions do a good job predicting nanoparticle agglomeration in
the .mu.-SLS powder bed.
[0157] One method to overcome the agglomeration effects due to van
der Waals interactions is to dispense the nanoparticles as part of
a colloidal solution and then to dry the solution to form the
powder layer. To test this method, a commercially available
colloidal solution of copper nanoparticles (Applied Nanotech) was
spin coated onto a silicon substrate and was dried on a hotplate.
As can be seen in FIG. 15B, this method of spreading the copper
nanoparticles produces a much more continuous and uniform
nanoparticle layer than the powder spreading method. This result
matches well with the predictions made by the no van der Waals
force discrete element simulation models. Overall, based on this
result, it may be possible to create much more uniform nanoparticle
beds for .mu.-SLS using a solution-based deposition method such as
spin coating or slot-die coating than by using more traditional
powder spreading methods, such as the use of a counter-rotating
roller or a doctor blade to spread a dry powder, which are commonly
used in larger scale SLS operations.
[0158] Results and Discussion
[0159] Another process in determining how nanoparticles sinter in
the .mu.-SLS bed is determining how heat is transferred within the
bed. In order to determine the mechanisms for heat transfer within
the bed, several particle-level simulations of the sintering
process were set up with both well-ordered and disordered
nanoparticle distributions. FIGS. 16A, 16B, 16C, 16D show a plot of
simulated electric field phasor (FIG. 16C) and temperature profile
(FIG. 16A) for loosely packed particle bed with uniform particle
distribution showing good heat transfer into the bulk of the powder
bed (FIG. 16D). Temperature distribution in a disordered powder bed
as a laser is scanned over its surface, showing very little heat
transfer into the bulk of the powder bed when near-field effects
not considered.
[0160] In the ordered NP simulation of the laser heating of the NP
powder bed where the effects of convection, conduction, and both
far-field and near-field radiation are considered in modeling heat
transfer within the NP bed, a temperature drop of only
.about.100.degree. C. was observed over the first 10 layers
(.about.1 .mu.m) of the NP bed. A similar simulation of a
disordered system that did not consider the effects of near-field
radiation found that heat did not penetrate more than two NP layers
into the bed. This data strongly suggests that near-field radiation
plays a key role in nanoparticle sintering and that if near-field
radiation effects are not included in the simulation it is more
difficult for heat to penetrate into the NP bed.
[0161] Another step in being able to model the .mu.-SLS process is
being able to model full part formation. This is done by taking the
optical, thermal, and sintering properties generated for the powder
bed from the particle level simulations and experimental results
and importing them into a continuum level simulation of the part
fabrication process. Continuum models use volume-averaged bulk
material properties to represent the behavior of the powder within
each finite volume of the simulation, thus avoiding the need to
resolve every powder particle individually. Without wishing to be
bound to particular theory, this is advantageous since powder
particles are several orders of magnitude smaller than the part
being produced, which makes resolving individual particles
computationally infeasible when simulating a full-part build. FIG.
17 shows a part that has been built using this continuum modeling
approach. This part was formed by scanning the laser in a square
pattern for each build layer. The model shows that a square part is
not produced by the square pattern because the longer laser dwell
times near the corners of the part over exposes those portions of
the part. This is a well-known experimental result. These results
support the feasibility of combining particle-level simulations and
measurements with continuum models in order to be able to generate
accurate part geometry and part property predictions.
[0162] Without wishing to be bound to particular theory, new
nanoscale physics present in the .mu.-SLS process fundamentally
change the mechanisms of part formation in .mu.-SLS as compared
with macro-SLS and should be considered in modeling final part
shape/quality. In an aspect, sintering is driven by grain boundary
and surface diffusion as opposed to particle melting. In another
aspect, light penetration into the particle bed is driven by
scattering and plasmonic effects as opposed to ray optics. In
another aspect, heat transfer within the particle bed is dominated
by near-field effects as opposed to simple conduction as assumed in
macroscale SLS process modeling. Discrete element modeling,
experimental verification, and continuum-level modeling can be used
to construct a model of the .mu.-SLS that incorporates nanoscale
effects, while also creating simulations that can model full-part
formation fast enough to be viable in the manufacturing
environment.
[0163] Exemplary micro-SLS System
[0164] FIG. 18 is a diagram of an exemplary micro-selective laser
sintering system 100 in accordance with an illustrative embodiment.
As shown in FIG. 18, the .mu.-SLS system 100 includes (1) a
spreader mechanism 102 configured to generate the powder bed, (2)
an optical system 104 (also referred to as an optical sintering
system) configured to write features into the powder bed, (3) an
ultrafast laser system 106 configured to sinter the particles (4) a
positioning system 108 configured to move and position a build
stage 112 between the optical system 104 and the spreader mechanism
102, and (5) a vacuum and vibration isolation 110 systems
configured to reduce outside influences that could damage the part
quality.
[0165] Still referring to FIG. 18, the nanopowder spreader
mechanism 102, in some embodiments, includes a slot die coating
system 102 (shown as "slot die coater 120" and "dispensing pump
122") configured to spread uniform layers of nanoparticle inks over
a workpiece 114 (shown as "a silicon wafer 114"). The slot die
coating system 102 is configured to dispense, in some embodiments,
a uniform layer of nanoparticle ink or a colloid comprising
nanoparticles suspended or mixed in a solvent. Upon drying (i.e.,
evaporation of the solvent), the nanoparticles in the nanoparticle
ink or colloid settle to form a uniform layer of nanoparticle
powder (shown as "powder bed 124"). The build stage 112, which
retains the workpiece 114, includes, in some embodiments, a heated
sample holder (shown as "heated chip holder 112") configured to
accelerate the drying of the nanoparticle inks or colloid to
produce the powder bed 124. The positioning system 108 includes, in
some embodiments, an electromagnetic linear actuator 116 configured
to move the silicon wafer workpiece 114 under the slot die coater
120. The positioning system 108 further includes, in some
embodiments, air bearings 118 configured to guide the motion and
ensure that a smooth uniform coating is produced. The positioning
system 108 positions the build stage 112 under the optical system
104 for sintering. In some embodiments, the positioning system 108
moves the build stage 112 under the optical system 104 as the
nanoparticle ink is drying. In other embodiments, the positioning
system 108 moves the build stage 112 under the optical system 104
after the nanoparticle ink has dried. The positioning system 108
includes, in some embodiments, a flexure-based nanopositioning
system configured to precisely move and align (e.g., in less 100 nm
resolution, e.g., 40 nm) the powder bed to the optical system 104
and the slot die coater 102 between each sintering operation. In
some embodiments, the optical system 104 is attached to a ball
screw and micro-stepper motor assembly configured to move the
projection optics up to compensate, after the sintering process,
for the increased height of the new layer that has been spread on
the powder bed.
[0166] FIGS. 19A and 19B, is a detail diagram of the exemplary
micro-selective laser sintering system 100 of FIG. 18 in accordance
with an illustrative embodiment. As shown in the FIG. 19A, the
build stage 112 is positioned, via the linear actuator 116, to a
first position 202 such the workpiece 114 is positioned proximal to
a dispensing head 204 of the slot die coater 120. The build stage
112, in some embodiments, is operatively coupled, via air bearings
240, to one or more guide rails 118. The slot die coater 120 is
configured to dispense, via a pump 206, from a tank 208,
nanoparticle ink or colloid comprising solvent with nanoparticles
mixed or suspended therein.
[0167] The build stage 112, in some embodiments, includes a XY
positioner 210 to provide fine positioning of the build stage 112
with respect to the slot die coater 120. In some embodiments, the
XY positioner 210 comprises an X-axis flexure member and a Y-axis
flexure member, each operatively coupled a voice coil 212. Each
X-axis and Y-axis flexure member is configured to elastically bend
along a respective direction (i.e., x-direction or y-direction). In
other embodiments, commercially-available 2-axis positioners having
less than 100 um resolution may be used. The build stage 112, in
some embodiments, includes a Z-axis nanopositioner 214. In some
embodiments, the .mu.-SLS system 100 includes sensors 216 (shown as
216a, 216b) to provide positioning signals (e.g., feedback signals)
to the XY flexure positioner 210 and Z-axis nanopositioner 214. In
some embodiments, the sensors 214 are interferometry sensors.
[0168] Referring still to FIG. 19A, the slot-die coater 120, in
some embodiments, is operatively coupled to a Z-axis actuator 218
configured to adjust the height displacement of the slot-die coater
120 in the Z-direction. In some embodiments, the Z-axis actuator
218 is configured to adjust the height of the slot-die coater 120
to compensate for each sintered layer added to the workpiece
114.
[0169] Referring now to FIG. 19B, the build stage 112 is
positioned, via the linear actuator 116, to a second position 222
such the workpiece 114 is positioned proximal to an objective lens
224 of the optical system 104. In some embodiments, the first
position 202 has a displacement that is greater than 1 foot (e.g.,
between 0.5 and 1 foot, between 1 and 2 feet, between 2 and 3 feet,
between 3 and 4 feet, between 4 and 5 feet, between 5-6 feet,
between 6 and 10 feet, and greater than 10 feet) from the second
position 222.
[0170] The build stage 112,l in some embodiments, includes a
heating element 236 (e.g., a thermoelectric device, e.g., peltier;
a resistive coil; or the like) to heat a surface 238 of the build
stage 112 in operative contact, or proximal to, the workpiece 114.
The heating element 236, in some embodiments, is configured to
accelerate the drying (or evaporation) of the dispensed
nanoparticle ink or solvent of the colloid to produce a uniform
layer of nanoparticle powder. A temperature sensor (not shown)
mounted to the build stage 112 or the surface 238, in some
embodiments, is used to provide feedback control for the heating
element 236. In some embodiments, the heat element 236 operates
continuously. In addition to accelerating the drying of the
dispensed nanoparticle ink or solvent of the colloid, the heat
element 236 may elevate the temperature of the workpiece, at an
elevate temperature as compared to ambient temperature, which may
reduce thermal stress between the workpiece and the layer being
sintered during the sintering process.
[0171] Referring still to FIG. 19B, the optical system 104 is
configured to direct a plurality of pulse lasers to the dispensed
layer of nanoparticles (i.e., the uniform layer of nanoparticle
powder formed from the dried nanoparticle ink or the dried colloid
of solvent and nanoparticle). The optical system 104 is operatively
coupled, in some embodiments, via fiber optics 226, to an ultrafast
laser 106. The optical system 104 includes one or more micro-mirror
array 228, comprising an array of addressable mirror elements, to
selectively direct the beam emitted from the laser 106 to the
workpiece 114. In some embodiments, the optical system 104 includes
a tube lens 230 to direct the reflected beam from the micro-mirror
array 228 to the objective lens 224. In some embodiments, the
.mu.-SLS system 100 includes sensors 232 (shown as 232a, 232b) to
provide positioning signals (e.g., feedback signals) to the XY
flexure positioner 210 and Z-axis nanopositioner 214 to align the
build stage 112 to the optical system 104. The optical system 104,
in some embodiments, is coupled to a Z-axis actuator 234 configured
to adjust the height displacement of the optical system 104 in the
Z-direction. In some embodiments, the Z-axis actuator 234 is
configured to adjust the height of the optical system 104 to
compensate for each nanoparticle powder layer added to the
workpiece 114. In some embodiments, the Z-axis actuator 234
includes a ball screw and micro-stepper motor assembly.
[0172] The .mu.-SLS system 100 includes one or more controller 220
to coordinate the operation of the slot-die coater, the optical
system, and various subcomponents of the micro-SLS system.
[0173] The controller may receive a computer-aid-design (CAD) file
or STL file having geometric description of the tangible object to
direct generation of the three-dimensional workpiece based on the
geometric description of the CAD file or STL file.
[0174] FIG. 20 depicts a diagram of a method 300 of operating the
.mu.-SLS system 100 in accordance with an illustrative embodiment.
The method 300 include, iteratively building, on a layer-by-layer
basis, the workpiece (e.g., 114) by incrementally applying a
uniform layer of nanoparticles via a slot-die coater (e.g., 120) on
top of the workpiece and incrementally sintering, on a selective
basis, over a broad area, the applied layer of nanoparticles via an
optical and laser system (e.g., 104 and 106).
[0175] Specifically, the method 300, at step 302, includes
positioning, via a linear actuator (e.g., 116), a build stage
(e.g., 112) at a first position (e.g., 102) such that the workpiece
114 located on the build stage (e.g., 112) is positioned proximal
to a dispensing head (e.g., 204) of a slot-die coater (e.g.,
120).
[0176] At the first position (e.g., 202), the system 100, at step
304, may align the workpiece (e.g., 114), via an X-Y-Z positioners
(e.g., 210, 214), to the head (e.g., 204) of the slot-die coater
(e.g., 120).
[0177] The system 100, at step 306, may dispense a uniform layer of
nanoparticle ink or colloid comprising a solvent having
nanoparticles mixed or suspended therein on top of the workpiece
(e.g., 114).
[0178] Conclusions
[0179] Exemplified methods and systems provides a particle-particle
interaction model to generate a random packing of nanoparticles and
an analysis of the packing fraction of Cu nanoparticles of given
particle size distribution by means of MFIX-DEM simulations was
presented. Herein, nanoparticles were injected into the domain from
the top boundary and allowed to fall under the influence of gravity
and van der Waals forces. Once the particles settle, their
positions and properties are can be used as an input for the
optical model. The extinction and effective absorption coefficient
of a powder bed hence can be calculated. The simulations were done
for different cases such as for pure copper nanoparticles, copper
nanoparticles with a polymer or oxide coating, and copper
nanoparticle in a colloidal coating. The coatings and treatments of
the nanoparticles can significantly affect the van der Waals
interactions between particles. The effects of various types of
particle size distributions (uniform, Gaussian, and log-normal)
were also studied for different standard deviations. The particles
in the simulation are assumed to not initially overlap and to not
initially be deformed due to the adhesion or contact effects. The
simulations are run until all particles settle on the surface and
find their final resting position. Contact forces are obtained by
Newton's laws based on the position, the linear, and the angular
velocities of each of the individual particles in the simulation. A
spring-dashpot model is used for particle interactions between the
nanoparticles and between the nanoparticles and the walls of the
simulation. The simulation takes an average time of 3*10.sup.5
seconds on an Intel 8-Core Xeon Processor.
[0180] Overall, these simulations show that van der Waals forces
have a significant influence on how nanoparticles agglomerate
within the .mu.-SLS powder bed. Nanoparticles subject to strong van
der Waals forces agglomerate very rapidly with multiple nucleation
points. This leads to non-optimal packing densities but relatively
small agglomerates. Nanoparticles subject to weaker van der Waals
forces still form agglomerates but the agglomerated assemblies are
generally larger and take longer to form than in the strong van der
Waals case due to the lower number of potential agglomeration
nucleation sites. When van der Waals interactions between the
nanoparticles are eliminated, such as in a colloidal suspension of
nanoparticles, the nanoparticles are able to form densely packed,
continuous nanoparticle layers as opposed to discrete agglomerated
particle assemblies. This result suggest a new potential method for
creating nanoparticle layers in .mu.-SLS additive manufacturing
systems using colloidal solutions. However, more work still needs
to be done to determine how well nanoparticles deposited from
colloidal solutions can be sintered together and to determine what
effect residual surfactants from the colloidal suspension might
have on the quality of the final sintered part.
[0181] FIG. 21 depicts non-exhaustive exemplary three-dimensional
parts that may be fabricated with the exemplified micro-SLS systems
and the methods.
[0182] Example Computing Device
[0183] FIG. 22 illustrates an exemplary computer that can be used
for predicting mechanical and electrical properties of parts
produced by selective laser sintering of powder beds. In various
aspects, the computer of FIG. 22 may comprise all or a portion of
the development workspace 100, as described herein. As used herein,
"computer" may include a plurality of computers. The computers may
include one or more hardware components such as, for example, a
processor 2021, a random access memory (RAM) module 2022, a
read-only memory (ROM) module 2023, a storage 2024, a database
2025, one or more input/output (I/O) devices 2026, and an interface
2027. Alternatively and/or additionally, controller 2020 may
include one or more software components such as, for example, a
computer-readable medium including computer executable instructions
for performing a method associated with the exemplary embodiments.
It is contemplated that one or more of the hardware components
listed above may be implemented using software. For example,
storage 2024 may include a software partition associated with one
or more other hardware components. It is understood that the
components listed above are exemplary only and not intended to be
limiting.
[0184] Processor 2021 may include one or more processors, each
configured to execute instructions and process data to perform one
or more functions associated with a computer for indexing images.
Processor 2021 may be communicatively coupled to RAM 2022, ROM
2023, storage 2024, database 2025, I/O devices 2026, and interface
b 2027. Processor 2021 may be configured to execute sequences of
computer program instructions to perform various processes. The
computer program instructions may be loaded into RAM 2022 for
execution by processor 2021. As used herein, processor refers to a
physical hardware device that executes encoded instructions for
performing functions on inputs and creating outputs.
[0185] RAM 2022 and ROM 2023 may each include one or more devices
for storing information associated with operation of processor
2021. For example, ROM 2023 may include a memory device configured
to access and store information associated with controller 2020,
including information for identifying, initializing, and monitoring
the operation of one or more components and subsystems. RAM 2022
may include a memory device for storing data associated with one or
more operations of processor 2021. For example, ROM 2023 may load
instructions into RAM 2022 for execution by processor 2021.
[0186] Storage 2024 may include any type of mass storage device
configured to store information that processor 2021 may need to
perform processes consistent with the disclosed embodiments. For
example, storage 2024 may include one or more magnetic and/or
optical disk devices, such as hard drives, CD-ROMs, DVD-ROMs, or
any other type of mass media device.
[0187] Database 2025 may include one or more software and/or
hardware components that cooperate to store, organize, sort,
filter, and/or arrange data used by controller 2020 and/or
processor 2021. For example, database 2025 may store hardware
and/or software configuration data associated with input-output
hardware devices and controllers, as described herein. It is
contemplated that database 2025 may store additional and/or
different information than that listed above.
[0188] I/O devices 2026 may include one or more components
configured to communicate information with a user associated with
controller 2020. For example, I/O devices may include a console
with an integrated keyboard and mouse to allow a user to maintain a
database of images, update associations, and access digital
content. I/O devices 2026 may also include a display including a
graphical user interface (GUI) for outputting information on a
monitor. I/O devices 2026 may also include peripheral devices such
as, for example, a printer for printing information associated with
controller 2020, a user-accessible disk drive (e.g., a USB port, a
floppy, CD-ROM, or DVD-ROM drive, etc.) to allow a user to input
data stored on a portable media device, a microphone, a speaker
system, or any other suitable type of interface device.
[0189] Interface 2027 may include one or more components configured
to transmit and receive data via a communication network, such as
the Internet, a local area network, a workstation peer-to-peer
network, a direct link network, a wireless network, or any other
suitable communication platform. For example, interface 2027 may
include one or more modulators, demodulators, multiplexers,
demultiplexers, network communication devices, wireless devices,
antennas, modems, and any other type of device configured to enable
data communication via a communication network.
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