A sintered body density measurement experiment is an experiment in which the density, porosity, and shrinkage of a sample obtained by compacting and firing a powder are measured to evaluate the progress of sintering.
In ceramics and powder materials, heating powder particles causes them to bond together, reducing voids and increasing densification.
The degree of this densification changes depending on firing temperature, firing time, compaction pressure, powder particle size, additives, atmosphere, and other factors.
In a discussion of sintered body density measurement, it is not sufficient simply to write that “the density increased” or “the sample shrank.”
It is necessary to explain why firing increases the density, why porosity decreases, how shrinkage is related to densification, and what the difference from theoretical density means.
In addition, when the Archimedes method is used, errors caused by open pores, closed pores, water penetration, bubbles, surface moisture, and other factors can also be discussed.
This article clearly explains, as examples of discussions that can be used in laboratory reports on sintered body density measurement, apparent density, bulk density, true density, relative density, porosity, shrinkage, sintering, densification, open and closed pores, the Archimedes method, firing conditions, causes of error, and points for improvement.
Note:
This article is a reference intended to assist with discussions of sintered body density measurement results obtained in inorganic materials chemistry experiments, ceramics experiments, materials engineering experiments, and powder compaction experiments at universities and similar institutions.
For the actual sample, firing temperature, firing time, density measurement method, Archimedes method procedure, and safety precautions, always follow the instructions in your university’s laboratory manual and those given by your instructor or TA.
- What Is Sintered Body Density Measurement?
- Main Items to Include in the Results
- Basic Concept of Density
- Difference Between Apparent Density, Bulk Density, and True Density
- Discussion of Relative Density
- Discussion of Porosity
- Difference Between Open and Closed Pores
- Discussion of Shrinkage
- What Is Sintering?
- Effect of Firing Temperature
- Effect of Firing Time
- Effect of Heating Rate
- Effect of Compaction Pressure
- Effect of Powder Particle Size
- Effects of Binders and Additives
- Discussion of the Archimedes Method
- Discussion of Water Absorption
- Relationship Between Sintered Body Density and Strength
- Overfiring and Abnormal Grain Growth
- Causes of Error in Sintered Body Density Measurement
- Reference Experimental Values and Calculation Examples for Sintered Body Density
- Reference Experimental Conditions
- Dimensional Measurement Results After Firing
- How to Calculate Shrinkage
- Example Calculation of Volumetric Shrinkage
- Measurement Results by the Archimedes Method
- Equations for Bulk Density, Water Absorption, and Apparent Porosity
- Calculation Example for Sample C
- Summary of Calculation Results
- Relationship Between Firing Temperature, Bulk Density, and Porosity
- Example of How to Write the Results
- Points for Connecting the Results to the Discussion
- Example Discussion
- Summary
- When the Results Can Be Considered Good
- Example Discussions When the Experiment Did Not Go Well
- How to Write Points for Improvement
- Difference Between a Superficial Discussion and a Good Discussion
- Examples of Expressions That Can Be Used in Reports
- Points to Check When Discussing Sintered Body Density Measurement
- Summary
What Is Sintered Body Density Measurement?
Sintered body density measurement is an experiment in which the density of a solid sample obtained by compacting and firing a powder is measured.
The density of a sintered body is an important indicator for evaluating how much void space remains inside the sample and how far densification has progressed.
The closer the density is to the theoretical density, the fewer the voids and the denser the sintered body is considered to be.
The density of a sintered body may be determined not only from its mass and external dimensions but also by the Archimedes method using its apparent weight in water.
Density calculated from external dimensions is easily affected by errors in shape measurement, while the Archimedes method is affected by water penetration into open pores and by bubbles.
It is important to understand the characteristics of the measurement method when discussing the results.
Example Discussion:
Sintered body density is an indicator of how far a powder compact has densified through firing.
A sample with higher density has fewer internal voids and is considered to have undergone more extensive interparticle bonding and material transport.
Therefore, comparing changes in density with firing temperature and firing time makes it possible to evaluate the progress of sintering.
Main Items to Include in the Results
In the results of sintered body density measurement, organize the type of powder, compaction method, compaction pressure, firing temperature, firing time, firing atmosphere, dimensions before and after firing, mass before and after firing, volume, density, relative density, porosity, and shrinkage.
If the firing conditions are varied, summarizing the results in a table for each condition makes the discussion easier.
Main Items to Include in the Results
- Powder material used
- Powder particle size
- Presence or absence of additives or binders
- Compaction method
- Compaction pressure
- Firing temperature
- Firing time
- Heating rate
- Firing atmosphere
- Dimensions before firing
- Dimensions after firing
- Mass before and after firing
- Apparent density
- Relative density
- Porosity
- Linear shrinkage or volumetric shrinkage
- Cracking or warping of the sample
- Causes of error and points for improvement
Example of How to Write the Results:
After the compact was fired, its dimensions became smaller than before firing and its density increased.
In addition, samples fired at higher temperatures showed greater shrinkage and lower porosity.
These results suggest that sintering progressed as the firing temperature increased, reducing interparticle voids and promoting densification.
Basic Concept of Density
Density is the mass per unit volume.
In a sintered body, even when the material is the same, a larger amount of internal void space causes the mass relative to the volume to become smaller and the density to decrease.
Conversely, as sintering progresses and the amount of void space decreases, the density increases.
Density = Mass / Volume
ρ = m / V
However, there are several ways of considering density in sintered bodies, including bulk density calculated from external dimensions, apparent density determined by the Archimedes method, and theoretical density of the material itself.
If the type of density being measured is not clearly identified, discussion of porosity and relative density becomes ambiguous.
Example Discussion:
Density is obtained by dividing mass by volume, and it decreases as the amount of void space inside a sintered body increases.
The increase in density after firing was considered to result from a decrease in interparticle voids caused by sintering, allowing the same material to occupy a smaller volume.
Therefore, an increase in density indicates progress of densification.
Difference Between Apparent Density, Bulk Density, and True Density
When considering the density of a sintered body, it is necessary to understand the difference between apparent density, bulk density, and true density.
Bulk density is the density calculated using the external volume of the sample and reflects the total volume including open and closed pores.
True density is the density of the solid portion of the material itself.
The meaning of apparent density may vary somewhat depending on the measurement method, but in general its value changes depending on how voids in the sample are treated.
In the Archimedes method, whether water enters open pores affects the measured value.
In a report, it is important to confirm the type of density defined in the laboratory manual and use the terminology accordingly.
| Type of Density | Meaning | Point for Discussion |
|---|---|---|
| Bulk density | Density using the external volume of the entire sample | The volume including open and closed pores affects the value |
| Apparent density | Measured density defined by the measurement method | Consider the effects of water penetration and bubbles |
| True density | Density of the solid portion only | Compare with theoretical density and material composition |
Example Discussion:
When considering the density of a sintered body, it is necessary to distinguish bulk density, which includes the external volume, from true density, which is closer to the density of the solid portion itself.
Because sintered bodies contain open and closed pores, the meaning of the measured density differs depending on the measurement method.
The density obtained in this experiment includes the effects of voids, so the difference from the theoretical density is considered to reflect the presence of remaining voids inside the sample.
Discussion of Relative Density
Relative density is a value indicating the percentage of the measured density relative to the theoretical density.
The theoretical density is the density assuming a completely dense material with no voids.
The higher the relative density, the closer the sintered body is to the theoretical density and the fewer the voids are considered to be.
Relative density = Measured density / Theoretical density × 100
A sample with a relative density close to 100% has undergone extensive densification.
On the other hand, a sample with low relative density may still contain many voids, may have been insufficiently fired, may have had a low green density, or may not have undergone sufficient particle sintering.
Comparing relative density at multiple firing temperatures makes it possible to quantitatively evaluate the progress of sintering.
Example Discussion:
The increase in relative density with increasing firing temperature was considered to result from increased material transport between particles and a reduction in voids.
The closer the relative density approaches the theoretical density, the more extensively the sintered body has densified.
However, because the relative density did not reach 100%, closed pores or residual voids were considered to remain even after firing.
Discussion of Porosity
Porosity is the proportion of the sample volume occupied by voids.
A higher porosity in a sintered body indicates that more pores remain inside.
A lower porosity indicates a denser material and may result in higher strength and durability.
Porosity = 100 – Relative density
Alternatively, Porosity = Void volume / Total volume × 100
Porosity tends to decrease as the firing temperature increases.
This is because neck growth progresses at the contact points between particles and the pores become smaller or become enclosed.
However, excessive firing may cause gas evolution or abnormal grain growth and may leave pores behind.
Example Discussion:
The lower porosity in samples fired at higher temperatures was due to a reduction in the voids between particles caused by sintering.
Material transport occurs at the contact points between particles and the necks grow, reducing the pore volume.
Therefore, the decrease in porosity indicates progress of densification in the sintered body.
Difference Between Open and Closed Pores
Voids inside a sintered body include open pores and closed pores.
Open pores are connected to the exterior and allow water or gas to enter.
Closed pores are not connected to the exterior and remain isolated inside the material.
In the early stage of sintering, many open pores exist between particles, and as sintering progresses, the pores may become smaller and change into closed pores.
In the Archimedes method, whether water enters open pores affects the measured value.
Because water does not easily enter closed pores, care is necessary when evaluating apparent density and porosity.
| Type of Pore | Characteristics | Effect on Measurement |
|---|---|---|
| Open pore | Connected to the exterior | Water readily enters and affects water absorption |
| Closed pore | Not connected to the exterior | Water does not enter and may prevent the density from reaching the theoretical value |
Example Discussion:
One possible reason why the density of the sintered body was lower than the theoretical density is that open and closed pores remained.
Open pores are connected to the exterior and allow water to enter, whereas closed pores are isolated inside and are difficult for water to penetrate.
Therefore, when measuring density by the Archimedes method, the presence of open and closed pores must be considered.
Discussion of Shrinkage
Shrinkage indicates how much the dimensions or volume of a sample decrease before and after firing.
As sintering progresses, the voids between particles decrease and the entire sample shrinks.
Therefore, shrinkage is an important indicator of the progress of sintering.
Linear shrinkage = (Length before firing – Length after firing) / Length before firing × 100
Volumetric shrinkage = (Volume before firing – Volume after firing) / Volume before firing × 100
Shrinkage may increase as the firing temperature increases.
This is because material transport is promoted, voids decrease, and the sample becomes denser.
However, excessive shrinkage may cause cracking, warping, or loss of dimensional accuracy.
Example Discussion:
The decrease in sample dimensions after firing was considered to result from a reduction in interparticle voids through sintering and from the particles moving closer together.
The greater shrinkage at higher firing temperatures indicates that material transport was promoted under the high-temperature conditions and densification progressed.
However, excessive shrinkage may also cause cracking or warping, so the firing conditions must be optimized.
What Is Sintering?
Sintering is a phenomenon in which powder particles bond together when a powder compact is heated to a high temperature, increasing its strength and density.
During sintering, necks form at the contact points between particles and grow through diffusion of atoms or ions.
As a result, the powder particles become integrated and the compact becomes a strong solid.
Sintering is not simply a phenomenon in which the powder melts because of heat and solidifies.
In many cases, material transport occurs in the solid state at temperatures below the melting point.
Processes such as grain-boundary diffusion, volume diffusion, surface diffusion, and evaporation-condensation are involved, reducing interparticle voids and promoting densification.
Example Discussion:
During sintering, necks form at the contact points between powder particles and diffusion strengthens the bonding between particles.
At higher firing temperatures, the movement of atoms or ions becomes more active, making neck growth and pore reduction easier to proceed.
As a result, the density of the sintered body increased and the shrinkage also became greater.
Effect of Firing Temperature
Firing temperature is one of the conditions that most strongly affects the density and porosity of a sintered body.
At low temperatures, material transport is insufficient and interparticle bonding and pore reduction do not proceed readily.
Therefore, density tends to remain low and porosity high.
Increasing the firing temperature promotes diffusion, neck growth, and particle rearrangement, increasing the density.
However, if the temperature is too high, abnormal grain growth, retention of closed pores, cracking caused by firing shrinkage, liquid-phase formation, or volatilization of components may occur.
It is important to select an optimal firing temperature.
Example Discussion:
The higher density of samples fired at higher temperatures was due to the promotion of interparticle diffusion and progression of sintering at high temperature.
Under low-temperature firing conditions, particle bonding was insufficient and many pores were considered to remain.
On the other hand, excessively high-temperature firing may cause grain growth or cracking, so not only density but also appearance and microstructure must be examined.
Effect of Firing Time
Firing time also affects the progress of sintering.
Even at the same temperature, longer firing times may allow interparticle diffusion to proceed further, reduce pores, and increase density.
With short firing times, sufficient densification may not occur and the density may remain low.
However, if the firing time is too long, grain growth may proceed excessively or closed pores may become trapped inside grains.
Energy consumption and dimensional changes may also become greater.
Firing time must be set by considering the balance between densification and grain growth.
Example Discussion:
The increase in density in samples fired for a longer time was considered to result from continued diffusion during firing and a reduction in interparticle pores.
However, prolonged firing may promote grain growth and make closed pores more likely to remain.
Therefore, firing time is a condition that promotes densification but also affects coarsening of the microstructure.
Effect of Heating Rate
Heating rate affects cracking, pores, and binder-removal behavior in a sintered body.
If a compact contains binder or moisture, rapid heating may cause gas or vapor to be generated inside the sample and lead to cracking or swelling.
In addition, a large temperature gradient may cause differences in thermal expansion between the interior and surface of the sample, making cracking more likely.
Slow heating allows dehydration and binder removal to proceed gradually and makes it easier to suppress internal defects.
However, if heating is too slow, the process takes longer and efficiency decreases.
When abnormalities are observed in the density or appearance of the sintered body, not only the firing temperature but also the heating rate should be discussed.
Example Discussion:
One possible reason why the sample cracked after firing is that the heating rate was too high and moisture or binder inside the sample was removed rapidly.
Rapid heating easily generates gas pressure and temperature differences inside the sample, causing cracking or swelling.
Therefore, to suppress defects in the sintered body, it is necessary to heat sufficiently slowly through the dehydration and binder-removal temperature ranges.
Effect of Compaction Pressure
Compaction pressure affects the density of the green compact before firing.
Higher compaction pressure packs the powder particles more densely and reduces the initial void space.
A green compact with high initial density tends to remain denser after firing.
However, if the compaction pressure is too high, residual stress or nonuniform pressure distribution may remain inside the compact.
As a result, cracking or lamination may occur during firing.
Compaction pressure requires a balance between increasing density and suppressing defects.
Example Discussion:
If the density after firing was higher in the sample compacted at higher pressure, the powder particles were considered to have been densely packed before firing and to have contained fewer initial voids.
The smaller the amount of initial void space, the less void volume must be eliminated during sintering, making densification easier.
However, excessive compaction pressure may cause internal stress or density nonuniformity and lead to cracking during firing.
Effect of Powder Particle Size
Powder particle size greatly affects sinterability.
Powders with smaller particle sizes have larger specific surface areas and higher surface energy, resulting in a greater driving force for sintering.
Therefore, finer powders may sinter more readily even at lower temperatures.
On the other hand, if the particles are too fine, they tend to agglomerate and may produce large voids or density nonuniformity in the green compact.
If the particle-size distribution is appropriate, smaller particles may fill the spaces between larger particles and increase the packing density.
Powder particle size and particle-size distribution affect both green density and sintered density.
Example Discussion:
If a higher density was obtained in the sample prepared using smaller particles, this was considered to result from the larger specific surface area and greater driving force for sintering.
Smaller particles have more contact points and neck growth by diffusion can proceed more readily.
However, if the powder is agglomerated, large voids may remain in the green compact and reduce the density after firing.
Effects of Binders and Additives
In powder compaction, binders, dispersants, and sintering aids may be added to improve compactability.
A binder increases the strength of the green compact but must decompose and be removed during firing.
If the binder is not properly removed, residual carbon, pores, or cracking may result.
Sintering aids may promote densification by forming a liquid phase at lower temperatures or accelerating diffusion.
However, if too much additive is used, secondary phases may form or segregation may occur at grain boundaries and change the material properties.
The effects of additives should be discussed not only from density but also together with crystal phases and mechanical properties.
Example Discussion:
If cracking occurred in a compact containing binder, rapid binder removal during firing may have generated gas inside the sample.
On the other hand, if a higher density was obtained in a sample containing a sintering aid, diffusion or liquid-phase formation may have been promoted and densification may have progressed.
However, because additives may also cause secondary-phase formation or grain-boundary segregation, the amount added must be optimized.
Discussion of the Archimedes Method
The Archimedes method is a method in which the volume of a sample is determined using the buoyant force acting on the sample when it is immersed in water, and the density is then calculated.
By measuring dry mass, submerged mass, and saturated mass, apparent density, water absorption, and open porosity may be determined.
One advantage is that the volume of samples with complicated external shapes can be determined relatively easily.
However, in the Archimedes method, errors may be caused by bubbles attached to the surface, insufficient water penetration, insufficient removal of surface water, dissolution of the sample, or changes in water density caused by temperature.
Particularly for porous samples, if water does not fully enter the open pores, the volume and density may not be evaluated correctly.
Volume = Mass in air – Mass in water
Density = Dry mass / Volume
*When the density of water is approximated as 1 g/cm3
Example Discussion:
In the Archimedes method, the sample volume is determined using buoyancy in water.
If bubbles adhere to the sample surface, the submerged mass is measured as too small and errors occur in the calculated volume and density.
In addition, if water does not sufficiently penetrate the open pores, the actual porous structure cannot be accurately reflected, so vacuum impregnation or a sufficient immersion time is important.
Discussion of Water Absorption
Water absorption is a value indicating how much water a sintered body absorbs.
A sample with high water absorption is considered to contain many open pores connected to the exterior.
As sintering progresses, open pores decrease and water absorption tends to decrease.
Water absorption = (Saturated mass – Dry mass) / Dry mass × 100
However, water absorption depends on how much water enters the open pores.
If the immersion time is short or bubbles remain, the measured water absorption may be lower than the actual value.
If surface water is not sufficiently wiped off, the water absorption is overestimated.
Example Discussion:
The lower water absorption in samples fired at higher temperatures was considered to result from a decrease in open pores caused by sintering.
In samples with many open pores, water enters the interior and increases the saturated mass.
On the other hand, as densification progresses, the number of pores connected to the exterior decreases and the amount of absorbed water becomes smaller, reducing the water absorption.
Relationship Between Sintered Body Density and Strength
The density of a sintered body is related to its mechanical strength.
In materials with high density and few voids, there is more solid material supporting the load and fewer defects that can act as fracture origins, so strength tends to become higher.
In contrast, materials with many voids are more likely to experience stress concentration and reduced strength.
However, high density does not necessarily mean high strength.
Particle size, grain-boundary condition, secondary phases, microcracks, and residual stress also affect strength.
Density measurement does not directly measure strength, but it is an important indicator for evaluating the quality of a sintered body.
Example Discussion:
A sintered body with high density tends to have higher strength because it contains fewer voids and more solid material supporting the load.
Voids act as fracture origins and stress-concentration sites, so samples with high porosity tend to have lower mechanical strength.
However, grain growth and microcracks also affect strength, so mechanical properties cannot be completely explained by density alone.
Overfiring and Abnormal Grain Growth
Overfiring may occur when the firing temperature or firing time is excessively high.
During overfiring, particles may grow too large or abnormal grain growth may occur.
As the particles become coarser, the grain-boundary area decreases and closed pores may become trapped inside the grains.
Overfiring may sometimes make the apparent density higher, but the microstructure becomes coarse and strength or thermal-shock resistance may decrease.
Warping, deformation, leakage of a liquid phase, or volatilization of components may also occur.
Results from high-temperature firing should be evaluated not only from density but also from appearance and microstructure.
Example Discussion:
If the increase in density leveled off in a high-temperature-fired sample, closed pores may have become trapped inside grains or abnormal grain growth may have progressed.
When sintering proceeds excessively, grain boundaries move and voids may become more difficult to remove to the exterior.
Therefore, increasing the firing temperature does not always cause density to continue increasing, and an optimal firing condition is considered to exist.
Causes of Error in Sintered Body Density Measurement
Causes of error in sintered body density measurement include errors in mass measurement, errors in dimension measurement, irregular sample shape, cracking or chipping, surface roughness, bubbles in the Archimedes method, insufficient water penetration into open pores, insufficient removal of surface water, changes in water temperature, and insufficient drying.
Because density is calculated from both mass and volume, errors in either measurement affect the result.
Particularly in porous samples, values obtained by the Archimedes method are affected by the condition of the open pores.
If bubbles adhere to the sample, the submerged mass becomes smaller and the density calculation deviates.
In addition, if the sample readily absorbs water, its mass may change during measurement.
It is important to standardize the drying state and immersion conditions before measurement.
Example Discussion:
Possible causes of variation in the density measurements include errors in dimensional measurement, chipping of the sample, bubble adhesion during the Archimedes method, and inconsistent wiping of surface water.
Sintered bodies may have rough and porous surfaces, and water penetration or attached bubbles can change the submerged mass.
Therefore, density measurement requires sufficiently drying the sample, removing bubbles, and measuring the mass under the same conditions.
Reference Experimental Values and Calculation Examples for Sintered Body Density
Here, reference experimental values are used to organize how the dimensions, shrinkage, bulk density, water absorption, and apparent porosity of a sintered body change with differences in sintering temperature.
In evaluating a sintered body, not only dimensional changes before and after firing but also changes in mass caused by immersion in water may be used to determine bulk density and apparent porosity.
As sintering progresses, the spaces between particles decrease, density generally increases, and porosity decreases.
Reference Experimental Conditions
| Item | Details |
|---|---|
| Sample shape | Cylindrical compact |
| Diameter before firing | 20.00 mm |
| Height before firing | 5.00 mm |
| Firing temperature | 1050°C, 1100°C, 1150°C, 1200°C |
| Holding time | 2 hours |
| Density and porosity measurement | Archimedes method using dry mass, saturated mass, and submerged mass |
Dimensional Measurement Results After Firing
First, the diameter and height before and after firing are measured to confirm dimensional changes caused by sintering.
As the sintering temperature increases, the diameter and height of the sample become smaller.
| Sample | Firing Temperature | Diameter After Firing | Height After Firing | Diameter Shrinkage | Height Shrinkage |
|---|---|---|---|---|---|
| A | 1050°C | 19.20 mm | 4.80 mm | 4.0% | 4.0% |
| B | 1100°C | 18.85 mm | 4.72 mm | 5.8% | 5.6% |
| C | 1150°C | 18.55 mm | 4.64 mm | 7.3% | 7.2% |
| D | 1200°C | 18.30 mm | 4.58 mm | 8.5% | 8.4% |
How to Calculate Shrinkage
Shrinkage expresses as a percentage how much smaller a sample becomes after firing relative to its dimensions before firing.
Shrinkage (%) = (Dimension before firing – Dimension after firing) / Dimension before firing × 100
For example, the shrinkage in the diameter direction of Sample C can be calculated as follows.
(20.00 – 18.55) / 20.00 × 100 = 7.25%
Rounded to one decimal place, the shrinkage in the diameter direction of Sample C is approximately 7.3%.
Example Calculation of Volumetric Shrinkage
For a cylindrical sample, the approximate volume can be calculated from the diameter and height.
Here, the volumetric shrinkage is calculated from the cylinder volumes before and after firing.
Volume of a cylinder = π × Radius² × Height
| Sample | Firing Temperature | Volume Before Firing | Volume After Firing | Volumetric Shrinkage |
|---|---|---|---|---|
| A | 1050°C | 1.571 cm³ | 1.390 cm³ | 11.5% |
| B | 1100°C | 1.571 cm³ | 1.316 cm³ | 16.2% |
| C | 1150°C | 1.571 cm³ | 1.254 cm³ | 20.2% |
| D | 1200°C | 1.571 cm³ | 1.204 cm³ | 23.4% |
The volumetric shrinkage shows that the volume decreases more as the firing temperature increases.
This is considered to result from the progression of sintering and reduction of the voids between particles.
Measurement Results by the Archimedes Method
Next, bulk density, water absorption, and apparent porosity are calculated using dry mass, saturated mass, and submerged mass.
Dry mass is the mass of a sufficiently dried sample, saturated mass is the mass measured in air after the sample has absorbed water, and submerged mass is the apparent mass measured in water.
| Sample | Firing Temperature | Dry Mass | Saturated Mass | Submerged Mass |
|---|---|---|---|---|
| A | 1050°C | 3.62 g | 3.96 g | 2.44 g |
| B | 1100°C | 3.70 g | 3.94 g | 2.49 g |
| C | 1150°C | 3.78 g | 3.92 g | 2.54 g |
| D | 1200°C | 3.83 g | 3.91 g | 2.58 g |
Equations for Bulk Density, Water Absorption, and Apparent Porosity
When the density of water is assumed to be 1.00 g/cm³, the external volume of the sample can be obtained from the difference between the saturated mass and the submerged mass.
External volume (cm³) = Saturated mass – Submerged mass
Bulk density (g/cm³) = Dry mass / External volume
Water absorption (%) = (Saturated mass – Dry mass) / Dry mass × 100
Apparent porosity (%) = (Saturated mass – Dry mass) / (Saturated mass – Submerged mass) × 100
Calculation Example for Sample C
For Sample C, the dry mass is 3.78 g, the saturated mass is 3.92 g, and the submerged mass is 2.54 g.
External volume = 3.92 – 2.54 = 1.38 cm³
Bulk density = 3.78 / 1.38 = 2.74 g/cm³
Water absorption = (3.92 – 3.78) / 3.78 × 100 = 3.7%
Apparent porosity = (3.92 – 3.78) / (3.92 – 2.54) × 100 = 10.1%
In this way, the proportion of open pores into which water can enter inside the sintered body can be evaluated using the dry mass, saturated mass, and submerged mass.
Summary of Calculation Results
| Sample | Firing Temperature | External Volume | Bulk Density | Water Absorption | Apparent Porosity |
|---|---|---|---|---|---|
| A | 1050°C | 1.52 cm³ | 2.38 g/cm³ | 9.4% | 22.4% |
| B | 1100°C | 1.45 cm³ | 2.55 g/cm³ | 6.5% | 16.6% |
| C | 1150°C | 1.38 cm³ | 2.74 g/cm³ | 3.7% | 10.1% |
| D | 1200°C | 1.33 cm³ | 2.88 g/cm³ | 2.1% | 6.0% |
Relationship Between Firing Temperature, Bulk Density, and Porosity
In this reference example, as the firing temperature increases from 1050°C to 1200°C, the bulk density increases from 2.38 g/cm³ to 2.88 g/cm³.
On the other hand, the apparent porosity decreases from 22.4% to 6.0%.
This is considered to result from the progression of sintering as the firing temperature increases, strengthening the bonding between particles and reducing the open pores inside the sample.
As sintering progresses, the sample becomes denser and the mass per unit external volume increases, so the bulk density increases.
Example of How to Write the Results
When the firing temperature was varied from 1050°C to 1200°C, the dimensions of the fired samples became smaller as the temperature increased.
The shrinkage in the diameter direction was 4.0% at 1050°C and 8.5% at 1200°C, showing that samples fired at higher temperatures underwent greater shrinkage.
The volumetric shrinkage also increased from 11.5% at 1050°C to 23.4% at 1200°C.
The bulk density determined by the Archimedes method was 2.38 g/cm³ at 1050°C and 2.88 g/cm³ at 1200°C, increasing with firing temperature.
On the other hand, the apparent porosity was 22.4% at 1050°C and 6.0% at 1200°C, decreasing at higher firing temperatures.
These results suggest that sintering progressed and the sample became denser as the firing temperature increased.
Points for Connecting the Results to the Discussion
In sintered body density measurement, it is important not only to present density and porosity values, but also to explain them in relation to firing conditions and changes in the material structure.
- Did the shrinkage increase as the firing temperature increased?
- Did the increase in shrinkage correspond to an increase in bulk density?
- Did apparent porosity and water absorption decrease as the firing temperature increased?
- Can the decrease in interparticle voids be attributed to high-temperature firing?
- Could excessive firing cause deformation, warping, cracking, or abnormal grain growth?
Example Discussion
In this experiment, the diameter and height of the sintered bodies decreased as the firing temperature increased, and the shrinkage increased.
This was considered to result from progression of interparticle bonding during firing and reduction of the voids that existed between particles.
In particular, the sample fired at 1200°C had the largest volumetric shrinkage at 23.4%, suggesting that densification through sintering had progressed.
In addition, the bulk density increased as the firing temperature increased, while the apparent porosity and water absorption decreased.
This was considered to result from a decrease in open pores at higher firing temperatures and a reduction in the amount of void space into which water could enter.
Therefore, bulk density, water absorption, and apparent porosity are effective indicators for evaluating the progress of sintering.
On the other hand, increasing the firing temperature does not always produce better results.
Excessive firing may cause deformation, warping, cracking, or grain growth.
Therefore, it is necessary to select an appropriate firing temperature according to the desired strength, porosity, and dimensional accuracy.
Summary
In evaluating a sintered body, shrinkage can be calculated from dimensional changes before and after firing, and bulk density, water absorption, and apparent porosity can be determined by the Archimedes method, allowing the progress of sintering to be quantitatively discussed.
As the firing temperature increases, shrinkage and bulk density generally increase, while water absorption and apparent porosity decrease.
Relating these changes to densification caused by sintering makes it possible to discuss the results based on experimental data.
When the Results Can Be Considered Good
Sintered body density measurement can be considered to have produced good results when consistent trends corresponding to the progress of sintering are obtained, such as an increase in density, a decrease in porosity and water absorption, and an increase in shrinkage with increasing firing temperature or firing time.
In addition, if the sample has no major cracks or chipping and the variation among repeated measurements is small, the results can be considered reliable.
However, the density may level off or even decrease on the high-temperature side.
In such cases, overfiring, retention of closed pores, abnormal grain growth, volatilization of components, or cracking should be considered.
In evaluating a sintered body, it is important to comprehensively consider density, porosity, shrinkage, appearance, and microstructure.
Example Discussion:
In this experiment, the density increased and the porosity decreased as the firing temperature increased.
In addition, dimensional shrinkage after firing also became greater, indicating that interparticle voids decreased and densification through sintering progressed.
Because these trends were consistent, the density measurement results were considered to accurately reflect the progress of sintering under the firing conditions.
Example Discussions When the Experiment Did Not Go Well
When sintered body density measurement does not go well, possible causes should be considered from results such as density lower than expected, low shrinkage, variation in measured values, cracking after firing, high water absorption, or failure of relative density to increase.
Organizing the causes according to the compaction, drying, firing, and measurement stages makes the discussion easier.
Example Discussion:
One possible reason why the density after firing was lower than expected is that the firing temperature or firing time was insufficient and interparticle diffusion and neck growth did not proceed sufficiently.
In addition, if the packing density during compaction was low, many initial voids were present and were more likely to remain after firing.
Therefore, the compaction pressure, powder particle size, and firing conditions must be optimized.
Another Example Discussion:
Possible causes of variation in density measurements by the Archimedes method include bubbles adhering to the sample surface and insufficient water penetration into open pores.
Errors may also occur if the method of wiping surface water before measuring the saturated mass is not consistent.
For porous samples, it is necessary to allow sufficient immersion time and remove bubbles before measurement.
Another Example Discussion:
Possible causes of cracking after firing include an excessively high heating rate, rapid removal of residual moisture or binder, and density nonuniformity inside the green compact.
In a sample with cracks or chipping, errors may occur in the external volume or volume determined by the Archimedes method, making accurate density evaluation difficult.
Therefore, drying and binder-removal processes before firing must be carefully controlled.
How to Write Points for Improvement
In a discussion of sintered body density measurement, writing not only the causes of error but also points for improvement makes the report easier to organize.
Points for improvement can be organized according to compaction, drying, firing, density measurement, and data processing.
Improvements to Compaction and Drying
- Mix the powder thoroughly
- Break up powder agglomerates
- Keep the compaction pressure constant
- Keep the amount of powder filled into the die constant
- Dry the compact sufficiently
- Do not remove the binder rapidly
Improvements to Firing Conditions
- Set an appropriate heating rate
- Control the firing temperature accurately
- Keep the firing time constant
- Consider the temperature distribution inside the furnace
- Keep the firing atmosphere consistent
- Avoid abnormal grain growth caused by overfiring
Improvements to Density Measurement
- Check the sample for chipping or cracking
- Measure mass accurately
- Measure dimensions at multiple locations
- Remove bubbles when using the Archimedes method
- Allow water to sufficiently penetrate open pores
- Use a consistent method for wiping off surface water
- Record the water temperature
- Calculate the mean and variation using multiple samples
Example of How to Write Points for Improvement:
To improve the reproducibility of sintered body density measurement, it is necessary to standardize the powder mixing condition, compaction pressure, drying conditions, firing temperature, and firing time.
In addition, in the Archimedes method, it is important to remove bubbles from the sample surface, allow water to sufficiently penetrate open pores, and keep the method of wiping off surface water consistent.
Presenting density, porosity, and shrinkage as average values from multiple samples makes it possible to evaluate the effects of firing conditions more reliably.
Difference Between a Superficial Discussion and a Good Discussion
In a discussion of sintered body density measurement, simply writing that “the density increased” or “the sample shrank” results in a superficial discussion.
A good discussion relates sintering, interparticle diffusion, neck growth, porosity, relative density, shrinkage, open and closed pores, and the measurement method.
| Superficial Discussion | Good Discussion |
|---|---|
| The density increased after firing. | Firing promoted interparticle diffusion and neck growth, reducing voids and causing densification, so the density of the sintered body increased. |
| The porosity decreased. | As sintering progressed, open pores between particles shrank or closed and the proportion of void volume in the total volume decreased, reducing the porosity. |
| The sample shrank. | The voids between particles decreased and the distance between particles became smaller, causing linear or volumetric shrinkage after firing. |
| The higher temperature was better. | At higher temperatures, material transport was promoted and densification progressed, increasing the density. However, excessively high temperatures may cause abnormal grain growth or retention of closed pores. |
| The measured value was incorrect. | Errors in dimensional measurement, chipping of the sample, bubbles in the Archimedes method, insufficient water penetration into open pores, and insufficient removal of surface water may have affected the density calculation. |
Examples of Expressions That Can Be Used in Reports
The following expressions can be used when writing the results and discussion of sintered body density measurement.
Adjust the necessary parts according to your own experimental results.
- Sintered body density is an important indicator of the progress of densification caused by firing.
- The increase in firing temperature promoted interparticle diffusion and was considered to have increased the density.
- The higher the relative density, the closer the sintered body is to the theoretical density and the fewer the voids.
- The decrease in porosity reflects the reduction of pores caused by sintering.
- The increase in shrinkage indicates that interparticle voids decreased and the compact became denser.
- Open pores are connected to the exterior and affect water absorption.
- Closed pores are difficult for water to penetrate and may prevent the density from reaching the theoretical value.
- In the Archimedes method, attached bubbles and surface water cause errors in density measurement.
- With excessive firing, the increase in density may level off because of grain growth or retention of closed pores.
- Evaluating density, porosity, and shrinkage together makes it possible to comprehensively judge the progress of sintering.
Points to Check When Discussing Sintered Body Density Measurement
Checking the following points before writing the report makes the discussion easier to write.
- Is the definition of density explained?
- Are apparent density, bulk density, and true density distinguished?
- Is relative density related to theoretical density?
- Are porosity and densification related?
- Is shrinkage explained in relation to the progress of sintering?
- Are the effects of firing temperature and firing time described?
- Are the effects of compaction pressure and powder particle size considered?
- Is the difference between open and closed pores explained?
- Are the causes of error in the Archimedes method considered?
- Are the effects of cracking or chipping on density measurement considered?
- Are overfiring and abnormal grain growth considered?
- Do the points for improvement correspond to the causes of error?
Summary
Sintered body density measurement is an experiment used to evaluate how far a powder compact has densified through firing.
As sintering progresses, necks form between particles and interparticle bonding becomes stronger through diffusion, while voids decrease.
As a result, density increases, porosity decreases, and shrinkage becomes greater.
Firing temperature, firing time, compaction pressure, powder particle size, heating rate, and additives greatly affect the density and porosity of a sintered body.
At low temperatures or short firing times, sintering is insufficient and voids tend to remain, while higher temperatures or longer firing times promote densification but may also cause overfiring or abnormal grain growth.
It is important to evaluate not only density but also porosity, shrinkage, water absorption, appearance, and the presence or absence of cracking.
In a report, rather than simply writing that “the density increased,” organize and discuss sintering, interparticle diffusion, neck growth, relative density, porosity, shrinkage, open and closed pores, the Archimedes method, firing conditions, measurement errors, and points for improvement.
Sintered body density measurement is an important experiment for understanding the relationship between densification of ceramic materials and firing conditions.
