In the thermodynamics analysis of diffusion in spark plasma sintering (SPS) welding of Cr3C2 (chromium carbide) and Ni (nickel), various thermodynamic principles and concepts are applied to understand the heat and mass transfer processes involved. SPS is a specialized technique used to consolidate powders into dense materials using pulsed direct current and pressure. The focus of the analysis is on diffusion, which refers to the movement of atoms or molecules from regions of high concentration to regions of low concentration. Diffusion plays a crucial role in the welding process of Cr3C2 and Ni, as it influences the formation of interfacial bonds between the particles. Thermodynamic analysis involves examining the energy changes and driving forces associated with diffusion during the SPS welding process. This analysis aims to determine the factors that govern the diffusion process, such as temperature, pressure, concentration gradients, and material properties. By studying the thermodynamics of diffusion, researchers can gain insights into the kinetics and mechanisms of atomic or molecular movement, as well as the resulting microstructural changes and bonding at the interfaces between Cr3C2 and Ni particles. This knowledge helps optimize the SPS welding process parameters and improve the quality and properties of the welded material. Key aspects explored in the thermodynamics analysis may include heat transfer mechanisms, such as Joule heating during SPS, and mass transfer phenomena, such as atomic diffusion of Cr, C, and Ni species. The analysis may also consider thermodynamic properties of the materials involved, such as melting points, phase diagrams, and chemical potential gradients, to understand the driving forces for diffusion. Overall, the thermodynamics analysis of diffusion in spark plasma sintering welding of Cr3C2 and Ni provides a deeper understanding of the fundamental principles governing the welding process, aiding in the development of advanced materials with enhanced properties and performance.

1. BET (Brunauer-Emmett-Teller)
Surface Analysis

2. Contents
 Introduction
 BET
 Adsorption
 Basic Principle
 Sample results
 Instrument schematic
 Results
 Applications

3. Introduction
01

4.  particles are only 1 to 100 nm across, different properties
begin to arise.
Introduction
 the surface area to volume is insignificant in relation to the
number of atoms in the bulk.
 commercial grade zinc oxide has a surface area range of 2.5
to 12 m2/g while nanoparticle zinc oxide can have surface
areas as high as 54 m2/g .
 superior UV blocking properties
 small size, making it very important to be able to determine
their surface area.

5. Hungarian chemist Stephen Brunauer (1903-
1986)
Hungarian born theoretical physicist Edward Teller (1908 –
2003)
American chemical engineer Paul H. Emmett (1900 -
1985)
American chemist and physicist Irving Langmuir (1881 - 1957)

6. 02 BET Theory

7. The Langmuir theory is based on the
following assumptions:
• All surface sites have the same
adsorption energy for the
adsorbate
• Adsorption of the solvent at one
site occurs independently of
adsorption at neighboring sites.
• Activity of adsorbate is directly
proportional to its concentration.
• Adsorbates form a monolayer.
• Each active site can be occupied
only by one particle.
𝜃 =
𝛼. 𝑃
1 + 𝛼. 𝑃
Schematic of the adsorption of gas
molecules onto the surface of a
sample showing
(a) the monolayer adsorption model
assumed by the Langmuir theory
and
(b) (b) s the multilayer adsorption
model assumed by the BET

8. In BET surface area analysis,
nitrogen is usually used because
of its availability in high purity and
its strong interaction with most
solids. Because the interaction
between gaseous and solid
phases is usually weak, the
surface is cooled using liquid
N2 to obtain detectable amounts
of adsorption.
Highly precise and accurate
pressure transducers monitor
the pressure changes due to the
adsorption process. After the
adsorption layers are formed,
the sample is removed from the
nitrogen atmosphere and heated
to cause the adsorbed nitrogen
to be released from the material
and quantified.

9.  Gas adsorption or Nitrogen adsorption
 Directly measures surface area & pore size distribution
 BET theory deviates from ideal to actual analysis
 Homogeneous surface
 No lateral interactions between molecules
 Uppermost layer is in equilibrium with vapour phase
 First and Higher layer: Heat adsorption
 All surface sites have same adsorption energy for adsorbate
 Adsorption on the adsorbent occurs in infinite layers
 The theory can be applied to each layer

10. 03
Adsorption

11. SPS current passes through the graphic die or the as-sintered
specimens and heats them through Joule heating. This endows
SPS with the following two remarkable advantages: low sintering
temperature and short sintering time relative to conventional
methods
it was sometimes found that in addition to the Coulomb force,
an extra driving force might exist enhancing the diffusion along
the direction of electron motion and inhibiting in the reverse
direction despite the type of charge owned by the diffusion
particle, thus producing a phenomenon similar to an “electron
wind.”
assumed that the bypassing current in SPS may reduce the activation energy
during processing by enhancing the mobility of defects and increasing the
point defect concentration. However, whether the small voltage of the
bypassing current, within 20V in SPS, did the same work with that in PAS,
about 10×10+3
V, was not discussed.

12. 02
EXPERIMENTAL
PROCEDURES

13. ● Initially, the plates were fine polished and
ultrasonically cleaned successively with
hydrochloric acid and alcohol. Further, the
sandwich diffusion couples were placed in the SPS
apparatus.
● To improve the precision of measuring the temperature, a K-type thermal couple
was pushed into the die as shown in Fig. 1. The tip of the K-type thermal couple
was located in line with the Cr3C2 plate and very close to it.
FIG. 1. The assembling sketch of the
specimens, graphic die, and thermal couple;
(a) with bypassing current and
(b) without bypassing current.

14. Owing to the small gap between
the heater and the specimens and
the excellent thermal conductivity
of insulating boron nitride plates, a
similar heating rate of about 100 C
min1 was achieved in this setup
(a) and (b), with or without
bypassing current, respectively.
The holding temperature varied
from 900 to 1200 C, with a
holding time of 10 min and was
followed by natural cooling to
room temperature. A small
pressure of about 5MPa was
used to ensure stable contact of
all the components described
above. Moreover, all runs were
performed under vacuum with a
residual pressure of less than 10
Pa.

15. After cutting, the microstructure of welded specimens was investigated
by scanning electron microscopy (SEM) and elemental distribution along
the height by energy dispersive X-ray spectroscopy (EDS) at the
interface. Ten parallel scanning lines were performed in the EDS
analysis in every specimen. The phase at the welding interface was
analyzed by X-ray diffraction (XRD) with the specimens prepared by
layer-by-layer polishing methods.

16. 03 EXPERIMENTAL
RESULTS

17. FIG. 2. The typical microstructure, phase analysis, and elemental distribution
images of the welded Cr3C2/Ni couples.
(a) SEM image of the upper interface at 1200 C;
(b) SEM image of the lower interface at 1200 C;
(c) XRD pattern of different samples;
(d) The EDS of the upper interface at 1200 C).

18. FIG. 3. Diffusion thicknesses and related empirical diffusion
coefficients vs. welding temperature
(a) Diffusion distances;
(b) Diffusion coefficients).

19. ∁(0,0)= 1 = ∁0
∁(𝑥,𝑡)= ∁0erfc(𝑥
2 𝐷𝑡
)
● Clearly, the diffusion distance and the diffusion coefficient both increase with
temperature in all runs, and exhibit obvious dependence on the current and its direction.
● At the welding temperature of 1200 ℃ and holding time of 10 min, the diffusion distance
and the diffusion coefficient with bypassing current were found to be 18 𝜇𝑚 and 8.25×
10−18
𝑚2
𝑠−1
, respectively, for the upper interfaces, and 12 𝜇𝑚 and 2.52× 10−18
𝑚2
𝑠−1
,
for the lower interfaces.
𝐷 = 𝐷0exp(
−𝐸𝐴
𝐾𝑇
)
● in which EA is the activation energy for diffusion, T is the absolute
temperature, and k is the Boltzmann constant. Obviously, there
must be some other factor besides the temperature relating the
current which also affects the diffusion; therefore, the EA also
changed.

20. An effect depending on current direction, for e.g., coulomb
force or “electron wind,” and an effect independent of current
direction possibly both occurred in this study. Moreover, the
contribution of the effect independent of current direction
offsets that of the effect depending on current direction at the
lower interface with bypassing current. It is extremely difficult
to separate the contribution of the bypassing current
(Coulomb force, the “electron wind,” the inducing defect, and
the local high temperature or temperature gradient) to the
atomic diffusion qualitatively; therefore, quantitative analysis
is usually required.

21. 04
MODEL OF THE DIFFUSION
ENHANCEMENT BY
BYPASSING CURRENT

22. Herein, we proposed a new model based on the Coulomb force and the local
high temperature and LTG. According to Fick’s equation relative to steady
diffusion, the atomic flux with bypassing current can be written as follows:
𝐽𝑖 = −
𝐷𝐶𝑖
𝑅
𝜕
𝜇𝑖
𝑇
𝜕𝑥
±
𝐹𝑍𝑖
∗
𝐸
𝑇
1
2
3
4
5
6
𝜕
𝜇𝑖
𝑇
𝜕𝑥
=
1
𝑇
𝜕𝜇𝑖
𝜕𝑥 𝑇
−
𝜇𝑖𝜕𝑇
𝑇2𝜕𝑥
𝜇𝑖|𝑇 = 𝑅𝑇𝑙𝑛𝐶𝑖
𝜕𝜇𝑖
𝜕𝑥 𝑇
=
𝑅𝑇𝜕𝐶𝑖
𝐶𝑖𝜕𝑥
𝐽𝑖 = −
𝐷𝐶𝑖
𝑇𝑅
𝑅𝑇𝜕𝐶𝑖
𝐶𝑖𝜕𝑥
− 𝑅𝑙𝑛𝐶𝑖
𝜕𝑇
𝜕𝑥
± 𝐹𝑍𝑖
∗
𝐸
𝐾𝑐𝐴𝑐
𝜕𝑇
𝜕𝑥
= 𝐼2
𝑅∗

23. 9 10
11 12
13 14
7 8
𝜕𝑇
𝜕𝑥
=
𝐼2
𝑅0𝜕𝐶𝑖
𝐾𝑐𝐴𝑐𝜕𝑥
𝐹𝑍𝑖
∗
E = 𝐹𝑍𝑖
∗ 𝜕𝑈
𝜕𝑥
= 𝑅0𝐹𝑍𝑖
∗
I
𝜕𝐶𝑖
𝜕𝑥
𝐽𝑖 = −𝐷
𝜕𝐶𝑖
𝜕𝑥
1 −
𝐼2
𝑅0
𝑇𝐾𝑐𝐴𝑐
𝐶𝑖𝑙𝑛𝐶𝑖 ±
𝐼2
𝑅0𝐹𝑍𝑖
∗
𝑅𝑇
𝐶𝑖
𝑅∗
= 𝑅0
𝜕𝐶𝑖
𝜕𝑥
𝐼2
𝑅0
𝑇𝐾𝑐𝐴𝑐
𝐶𝑖𝑙𝑛𝐶𝑖
𝐼2
𝑅0𝐹𝑍𝑖
∗
𝑅𝑇
𝐶𝑖
𝐷1 = 𝐷0 1 + 𝐾1𝐼2
+ 𝐾2𝐼
𝐷2 = 𝐷0 1 + 𝐾1𝐼2
+ 𝐾2𝐼
∆𝐷 =
𝐷1+𝐷2−2𝐷0
𝐷0
~ 𝐼2

24. FIG. 4. Electric resistance of the couple Ni-x%Cr3C2/Ni (X=10,
30, 50, 70, 90, and 100) welded at 800℃
FIG. 5. The experimental and calculated diffusion
coefficient ratios as functions of temperature.
FIG. 6. Profile of ∆D ~ 𝐼2
with the experimental data from
Fig. 5.

25. CONCLUSION

26. Results showed that the Ni diffusion coefficient in
Cr3C2 with a bypassing current of 1086A at a
temperature of 1200℃was 8.25× 10−18
𝑚2
𝑠−1
and
2.52 × 10−18
𝑚2
𝑠−1
at the upper and lower
interfaces of the sandwich couple, respectively.
The diffusion coefficient for both interfaces without
a bypassing current was 1.69× 10−18
𝑚2
𝑠−1
.
the bypassing current on the diffusion
involved a symmetric contribution from the
Coulomb force and a directionally
independent positive contribution from an
unknown driving force. this unknown X-
force was explained through a newly
proposed model based on the LTG.
A mass diffusion equation with
contributions from the traditional
concentration gradient, Coulomb force,
and LTG, which was caused by the
bypassing current, was derived within the
traditional physical theory.
Both the qualitative and quantitative analyses of
the as-deduced equation showed good
consistency with the experimental results in the
present study and with previous results from the
literature reports.

27. Thanks!

28. Live as if you were to die tomorrow.
Learn as if you were to live forever.
Mahatma Gandhi