# US 2017/0282247 A1 · Modeling of nanoparticle agglomeration and powder bed formation in microscale selective laser sintering systems

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- Number: US 2017/0282247 A1
- Document ID: US20170282247A1
- Status: Published application
- Kind: A1
- Application number: 15/475,807
- Filed: 2017-03-31
- Published: 2017-10-05
- Earliest claimed: 2016-04-01
- Assignees: Board of Regents, The University of Texas System
- Applicants: Board of Regents, The University of Texas System
- Inventors: Michael A. Cullinan; Anil Yuksel; Nilabh Kumar Roy
- Web page: https://patentgrep.com/patent/US20170282247A1

## CPC

- B22F 7/02: of composite layers {(B22F7/002 takes precedence)}
- B22F 10/28: Powder bed fusion, e.g. selective laser melting [SLM] or electron beam melting [EBM]
- B22F 10/36: of energy beam parameters
- B22F 10/68: Cleaning or washing
- B22F 10/73: of powder
- B22F 12/17: to heat the build chamber or platform
- B22F 12/22: {Driving means}
- B22F 12/44: characterised by the configuration of the radiation means
- B22F 12/49: Scanners
- B22F 12/53: Nozzles
- B22F 12/90: Means for process control, e.g. cameras or sensors
- B23K 1/0008: {specially adapted for particular articles or work}
- B33Y 10/00: Processes of additive manufacturing
- B33Y 30/00: Apparatus for additive manufacturing; Details thereof or accessories therefor
- B33Y 50/02: for controlling or regulating additive manufacturing processes
- B33Y 70/00: Materials specially adapted for additive manufacturing
- B33Y 80/00: Products made by additive manufacturing
- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- H10P 72/0436: {mainly by radiation}
- H10W 70/05: of insulating or insulated package substrates, or of interposers, or of redistribution layers (manufacture or treatment of leadframes H10W70/04)
- H10W 70/099: {Connecting interconnections to insulating or insulated package substrates, interposers or redistribution layers}
- H10W 70/688: {Flexible insulating substrates}
- H10W 74/012: {of encapsulations on active surfaces of flip-chip devices, e.g. forming underfills}
- H10W 74/016: {using moulds}
- H10W 74/121: {by multiple encapsulations, e.g. by a thin protective coating and a thick encapsulation}
- H10W 74/15: on active surfaces of flip-chip devices, e.g. underfills
- B22F 1/07: Metallic powder characterised by particles having a nanoscale microstructure (nanosized particles B22F1/054)
- B22F 12/45: Two or more
- B22F 2999/00: Aspects linked to processes or compositions used in powder metallurgy
- B23K 2101/36: Electric or electronic devices
- H10P 72/0446: {Apparatus for mounting on conductive members, e.g. leadframes or conductors on insulating substrates}
- H10P 72/78: using vacuum or suction, e.g. Bernoulli chucks
- H10W 46/00: Marks applied to devices, e.g. for alignment or identification
- H10W 46/301: {for alignment}
- H10W 72/01357: {by reflowing or heating}
- H10W 72/016: {of strap connectors}
- H10W 72/07118: {Means for cleaning, e.g. brushes}
- H10W 72/07125: {Means for controlling the bonding environment, e.g. valves or vacuum pumps}
- H10W 72/07141: {Means for applying energy, e.g. ovens or lasers}
- H10W 72/07183: {Means for monitoring}
- H10W 72/072: {of bump connectors}
- H10W 72/07202: {using auxiliary members}
- H10W 72/07223: {Active alignment, e.g. using optical alignment using marks or sensors}
- H10W 72/07231: {Techniques}
- H10W 72/07235: {Applying EM radiation, e.g. induction heating or using a laser}
- H10W 72/07236: {Soldering or alloying}
- H10W 72/07302: {using an auxiliary member}
- H10W 72/07323: {Active alignment, e.g. using optical alignment using marks or sensors}
- H10W 72/07331: {Connecting techniques}
- H10W 72/07335: {Applying EM radiation, e.g. induction heating or using a laser}
- H10W 72/07341: {Controlling the bonding environment, e.g. atmosphere composition or temperature}
- H10W 72/241: {Dispositions, e.g. layouts}
- H10W 99/00: Subject matter not provided for in other groups of this subclass
- Y02P 10/25: Process efficiency
- B22F: WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER (making alloys by powder metallurgy C22C); APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
- B23K: SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B33Y: ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- H10P: GENERIC PROCESSES OR APPARATUS FOR THE MANUFACTURE OR TREATMENT OF DEVICES COVERED BY CLASS H10
- H10W: GENERIC PACKAGES, INTERCONNECTIONS, CONNECTORS OR OTHER CONSTRUCTIONAL DETAILS OF DEVICES COVERED BY CLASS H10
- Y02P: CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS

## Abstract

Exemplified microscale selective laser sintering (μ-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.

## Claims

### Claim 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.

### Claim 2 (depends on 1)

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.

### Claim 3 (depends on 1)

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.

### Claim 4 (depends on 1)

The method of claim 1, wherein the plurality of nanoparticles are substantially spherical in shape.

### Claim 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.

### Claim 6 (depends on 5)

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.

### Claim 7 (depends on 5)

The method of claim 5, wherein the discrete element model facilitates analysis of nanoparticle beds as a whole distribution under dominant nanoscale force interactions.

### Claim 8 (depends on 5)

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.

### Claim 9 (depends on 5)

The method of claim 5, comprising:
optimizing critical parameters for selective laser sintering process to achieve micro-scale features.

### Claim 10 (depends on 5)

The method of claim 5, comprising:
optimizing critical parameters for selective laser sintering process to achieve sub-micron-scale features.

### Claim 11 (depends on 5)

The method of claim 5, comprising:
predicting, via the processor, locations of the nanoparticle at steady state.

### Claim 12 (depends on 11)

The method of claim 11, comprising:
performing, via the processor, thermal simulation using the locations of the nanoparticle at steady state.

### Claim 13 (depends on 5)

The method of claim 5, wherein the DEM model comprises a number of spherical particles, Nm, with diameter, Dm, and density, ρsm, wherein each of the N particles is defined within a Lagrangian reference at time t by its position, X(i)(t), linear velocity, V(i)(t), angular velocity, ω(i)(t), diameter, D(i), density ρ(i), and mass m(i); to position, linear velocity and angular velocities of the ithparticle change with time according to Newton's laws as:
dX
(
i
)

(
t
)
dt
=
V
(
i
)

(
t
)
m

(
i
)

dV
(
i
)

(
t
)
dt
=
F
T

(
i
)
=
m
(
i
)

g
+
F
d
(
i
)

(
t
)
+
F
c
(
i
)

(
t
)
I
(
i
)

d


ω
(
i
)

(
t
)
dt
=
T
(
i
)
wherein a total drag force, Fd(i), is found by a summation of pressure and viscous forces, and wherein a net contact force, Fc(i), is a force acting on the particle as a result of contact with other particles and a total force on each particle, FT(i), is found through a summation of all forces acting on an ithparticle.

### Claim 14 (depends on 5)

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:
δ
n
,
ij
=
4
3

E
m

E
l

r
m


l
E
m

(
1
-
σ
l
2
)
+
E
l

(
1
-
σ
m
2
)

δ
n
,
ij
1
/
2
k
t
,
ij
=
16
3

G
m

G
l

r
m


l
G
m

(
2
-
σ
l
)
+
G
l

(
2
-
σ
m
)

δ
n
,
ij
1
/
2
wherein Emand El are elastic moduli, and σm and σl are Poisson ratios for mth and lth nanoparticles.

### Claim 15 (depends on 5)

The method of claim 5, wherein coefficients of normal restitution matrix and tangential coefficient of restitution are written as M×M symmetric matrices for M solid-phases.

### Claim 16 (depends on 5)

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

π


ϕ


R
(
(
Asperities
Asperities
+
R
)
+
1
(
1
+
Asperities
r
inner


cutoff
)
2
)
wherein A is the Hamaker constant, R is an equivalent radius, r is a separation distance, φ is a surface energy, D is a particle diameter, rPinner cutoff and rPouter 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 rWinner cutoff and rWouter cutoff are the inner and outer cutoff value between particle-wall interactions.

### Claim 17 (depends on 5)

The method of claim 5, wherein the size distribution is modeled as a Gaussian distribution.

### Claim 18 (depends on 5)

The method of claim 5, wherein the size distribution is modeled as a log-normal distribution.

### Claim 19 (depends on 5)

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.

### Claim 20 (depends on 15)

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(i)and X(j), and have radii Ri and Rj, are considered neighbors upon satisfying condition:
|X(i)−X(j)|<K(Ri+Rj)
wherein K is an interaction distance constant.

### Claim 21 (depends on 5)

The method of claim 5, wherein the DEM includes nanoscale heat transfer analysis in modeling thermal properties of the powder bed with nanoparticles.