Solid state reactions involve reacting solids to form new solids and compounds. They have advantages like simple apparatus and low cost but also disadvantages like wide particle size distributions, need for high temperatures, and risk of contamination. Key factors that influence solid state reactions include particle size and distribution, mixing homogeneity, compaction between particles, and reaction temperature. Finer particle sizes and narrower distributions can promote more complete reactions at lower temperatures by increasing contact points between reactants.

1. Solid State Reaction: General
- Reaction between the solids
Advantages
1. Simple apparatus (ball milling,
A+B
rotatory evaporator)
2. Inexpensive (cost-effective)
Disadvantages
1. Wide particle-size distribution
2. Coarse particle size ( ≥1µm)
3. Contamination during mixing
4. High temperature is required for reaction
especially when the particle size is large
C+A+B
or when the mixing is insufficient
5. Compositional fluctuation due to
the incomplete reaction
6. Difficult to control the particle shape
Advanced Electronic Ceramics I (2004)
Rotatory evaporator
http://www.buchi-analytical.com/file/2/ct_1120_ctDownload1.pdf
Advanced Electronic Ceramics I (2004)

2. Solid State Reaction
AO
BO2
Starting powder Incomplete reaction Proper reaction Strong bond
due to excessive
reaction
ABO3
A+
AO BO2 AO BO2
L ∝ t1/2
B2+
L
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)
Solid State Reaction: Particle size
(1) coarse particles
AO
AO
ABO3
BO2 BO2
L ∝ t1/2
(2) fine particles
AO
ABO3
BO2
For complete reaction, t1 = 4t2
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)

3. Solid State Reaction: Particle-size distribution
At the presence of a coarse particle in a fine matrix particles
AO
ABO3
BO2 BO2
Strong bond between particles can be occurred
when the reaction time increased in order to achieve
complete reaction
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)
Solid State Reaction: mixing
(1) good mixing AO BO2
AO
ABO3
BO2
(2) bad mixing
AO
ABO3
BO2
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)

4. Solid State Reaction: other parameters
1. Compaction or filling state
- The reaction occurs and the contact points between two phase
2. Temperature
- the temperature dependence of diffusion coefficient
D = Do exp (-E/RT)
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)
Solid State Reaction: BaTiO3
Fig. In-situ X-ray diffraction
BL: γ-BaCO3, BH: β-BaCO3,
T: TiO2, B2T: Ba2TiO4,
BT: BaTiO3, BT3: BaTi3O7,
BaCO3:
BT4: BaTi4O9,
TiO2
B2T formation from ~800oC
BT formation from ~900oC
The completion of BT formation
: ~1200oC
Temperature (oC)
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)

5. Solid State Reaction: BaTiO3
Fig. In-situ X-ray diffraction
BL: γ-BaCO3, BH: β-BaCO3,
T: TiO2, B2T: Ba2TiO4,
BT: BaTiO3, BT3: BaTi3O7,
BT4: BaTi4O9,
BaCO3:
TiO2
Avg. size of BaTiO3: 1 µm
(A) avg. size of TiO2: 6.5 µm
(B) avg. size of TiO2: 2.0 µm
(C) avg. size of TiO2: 0.05 µm
In the case of fine powder,
- small B2T formation
- BT formation
Temperature (oC)
at low temperature
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)
Solid State Reaction: BaTiO3
Fig. In-situ X-ray diffraction
BL: γ-BaCO3, BH: β-BaCO3,
T: TiO2, B2T: Ba2TiO4,
BT: BaTiO3, BT3: BaTi3O7,
BT4: BaTi4O9,
BaCO3:
TiO2
The curves for the co-precipitated
BaTiO3 powder
- almost no intermediate reaction
- low temperature formation
Temperature (oC)
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)

6. Solid State Reaction: BaTiO3
1. Reaction at the contact points
In order to avoid the incomplete reaction,
- smaller particle size
- good mixing
- narrow particle-size distribution
- good compaction between particles
2. Reaction at relatively high temperature
- frequently results the milling the powder aggregates
for further process
- involves the contamination during ball milling
Ceramic Processing: Powder Preparation and Forming, Ceramic Society of Japan (1984)
Advanced Electronic Ceramics I (2004)