Determination of particle size of powders by optical microscope method

IS 5258: Scope - Key Formulas, Tables, and Specifications

1. Particle Size Conversions (Clause 1.2, Table A-1)

Conversion factors between different particle size measurement methods:

2. Size Classes (Clause 5.6.2, Table 1)

Use weighting factors for calculating size distributions.

3. Combined Sieve & Microscope Analysis (Clause 1.4, Table 9)

• Use multiplying factor 0.71 (Appendix A) to convert projected diameters to sieve sizes.
• Example: For a sieve size of 75 μm, projected diameter = 106 μm, weight passing = 45%.

Summary

• Particle size can be characterized by sieve, projected, or Stokes diameters.
• Use conversion factors for correlating sizes.
• Size classes help categorize particles for analysis.
• Combined sieve and microscope data provide detailed particle size distribution.

flowchart LR
    A[Sieve Size] -->|Multiply by 1.40| B[Projected Diameter]
    A -->|Multiply by 0.94| C[Stokes Diameter]
    B -->|Multiply by 0.71| A
    B -->|Multiply by 0.67|

IS 5258: Terms and Definitions - Key Points

1. Particle Size Definitions (Clause 1.2 & A-1.2):

   • Sieve Size: Nominal aperture size particle passes through.
   • Projected Diameter: Diameter of a circle equal to particle's projected area in stable position.
   • Stokes Diameter: Diameter of sphere with same density and settling velocity in fluid (Stokes' law).

2. Shape Factor Conversion Table:
   | From → To | Sieve | Projected | Stokes | |-----------|-------|-----------|--------| | Sieve | 1 | 1.40 | 0.94 | | Projected | 0.71 | 1 | 0.67 | | Stokes | 1.07 | 1.50 | 1 |

3. Size Classes (Clause 5.6.2, Table 1):

   • Size classes range from 0.59 to 149.9 microns with arithmetic means and weighting factors for distribution.
   • Weighting factors increase exponentially with size class (e.g., Class 1 = 0.36, Class 16 = 2,100,000).

4. Combined Sieve and Microscope Analysis (Clause 1.4, Table 9):

   • Use shape factor 0.71 to convert sieve diameter to projected diameter for combined size analysis.

Summary Formula for Conversion:

[ D_{\text{to}} = D_{\text{from}} \times \text{Shape Factor} ]

where shape factors are from the conversion table above.

flowchart LR
    A[Sieve Diameter] -->|x1.40| B[Projected Diameter]
    A -->|x0.94| C[Stokes Diameter]
    B -->|x0.71| A
    B -->|x0.67| C
    C -->|x1.07| A
    C -->|x1.50| B

This standard ensures consistent interpretation of particle sizes across testing methods.

IS 5258 Microscope Equipment Key Specifications & Tables

1. Microscope Requirements (Clause 5.1 & 5.1.1)

• Illumination source, coarse & fine focusing.
• Focusing & centering substage condenser with adjustable diaphragm.
• Mechanical stage with graduated movements readable to 0.1 mm.
• Objectives covering 0.6 to 150 microns particle size.
• Preferably focusing eyepiece with graticule and stage micrometer.
• Types:
  • Bench microscope with adjustable draw tube (140-200 mm).
  • Projection microscope with eyepiece graticule.
  • Projection microscope with graticule on projection screen.

2. Objective Lens Specifications (Clause 7.5.2 Table Extract)

3. Key Formulas & Notes

• Magnification (M) = Objective Magnification × Eyepiece Magnification.
• Numerical Aperture (NA) relates

IS 5258 — Sample Preparation Key Points

• Clause 4.2 & 8.1:

  • Prepare analysis sample per Appendix C (details sample handling and dilution).
  • Adjust particle concentration on the slide so each field of view contains ~6 particles of the size class examined.
  • Use lower concentration for number size distribution vs. weight size distribution.

• Clause 2.3:

  • Intermediate Sample: Portion of lab sample including the analysis sample, ensuring representativeness.

• Clause 4.1:

  • Laboratory sample preparation must follow IS 4879-1968 for representativeness of gross sample.

Practical Notes:

Sample Preparation Flow (Mermaid Diagram)

flowchart TD
    A[Gross Sample] --> B[Laboratory Sample (IS 4879)]
    B --> C[Intermediate Sample]
    C --> D[Analysis Sample (Appendix C)]
    D --> E[Slide Preparation with ~6 particles/field]
    E --> F[Microscopic Analysis]

This ensures representative and consistent particle size distribution analysis per IS 5258.

IS 5258: Microscope Setup & Illumination Key Points

Microscope Setup (Clause 5.1.1)

• Essential Components:

  • Illumination source with adjustable diaphragm
  • Coarse & fine focusing
  • Focusing & centering substage condenser with diaphragm
  • Mechanical stage with graduated movements (readable to 0.1 mm)
  • Objectives covering 0.6 to 150 microns
  • Focusing-type eyepiece with graticule
  • Stage micrometer for calibration

• Microscope Types:

  • Bench microscope with eyepiece graticule & adjustable draw tube (140-200 mm)
  • Projection microscope with eyepiece graticule and adjustable draw tube
  • Projection microscope with graticule on projection screen

Illumination (Clause 5.2)

• Use a homogeneous light source filling the entire field of view at lowest magnification.
• Adjustable diaphragm for controlling illumination.
• Use colored/neutral filters for color/intensity control.
• Monochromatic illumination recommended for particles < 2.3 microns.

Key Table Extract (Clause 7.5.2): Objective Magnification and Aperture

Formula for Magnification Matching

[ M = \frac{\text{Tube length}}{\text{F

IS 5258: Magnification and Objective Selection — Key Points

1. Magnification Matching Procedure (Clause 7.5.1 & 7.3.1)

• Select objective focal length from Table 7 for desired matching.
• Choose eyepiece power per Clauses 6.2, 6.3, and Table 2.
• Use a graticule with grid length matching size classes.
• Magnification at graticule plane adjusted in powers of √2 (relative magnifications from Table 6).
• Largest size class matching uses 32 mm or 25 mm objective (~4× to 6× magnification).

2. Key Tables

3. Example from Table 7 (Dry Objectives)

4. Minimum Numerical Aperture & Total Magnification (From Table 6)

IS 5258: Graticule Selection and Calibration Key Points

1. Graticule Dimensions (Clause 7.1.1 & Table 5)

• Grid length: 100 units
• Grid breadth: 50 units
• Distance between marks: 85.4 units
• Diameter of reference circles: Increase geometrically by factor √2 (approx. 1.41)

  Circle No.	Diameter (units)
  1	1.41
  2	2.00
  3	2.83
  4	4.00
  5	5.66
  6	8.00
  7	11.31

Units = 1/100th of grid length.

2. Calibration of Magnification (Clause 1.1 & Table 10)

• Magnification at graticule plane varies with eyepiece focal length.
• Relative magnification follows powers of 2 and √2.
• Example for focal length 31.6 mm:
  • Measured magnification: 4.24 to 5.88
  • Relative magnification: 1 (base)
  • Ratio (measured/relative): ~4.24 to 5.88

3. Specifications

• Physical size accuracy: ±2% on grid length.
• Graticule pattern per IS 5257-1969.
• Grid length chosen based on magnification and tube length (Appendix E).

Formula for circle diameters:

[ D_n = D_1 \times (\sqrt{2})^{n-1} ]

flowchart LR
    A[Start: Select Eyepiece Focal Length] --> B{Determine Magnification}
    B --> C[Calculate Relative Magnification (powers of 2, √2)]
    C --> D[Select Grid Length (Table 10)]
    D --> E[Use Table 5 for Circle Diameters]
    E --> F[Mark Graticule with ±2% accuracy]

Summary: Use Table 5 for graticule dimensions, Table 10 for magnification

IS 5258: Field Selection and Sampling Pattern

Key Points from Clauses:

• Clause 14.1.6:

  • Area of each field = area of the full rectangular grid of the graticule for control size class.
  • For other size classes, adjust field area per Clauses 14.1.4, 14.1.5, and Appendix G.

• Clause 7.1.1 & Table 5:

  • Grid length = 100 units (1 unit = 1/100th grid length)
  • Grid breadth = 50 units
  • Distance between marks = 85.4 units
  • Circle diameters increase geometrically by √2:

    Circle No.	Diameter (units)
    1	1.41
    2	2.00
    3	2.83
    4	4.00
    5	5.66
    6	8.00
    7	11.31

• Clause 8.3.1:

  • Sample fields must be spaced regularly to represent equal slide area proportions.
  • Fig. 3 (not shown) illustrates 25 fields spaced evenly over 20 mm × 20 mm.

• Sampling Pattern Formula:
  If total slide area = A, number of fields = n, then spacing between fields = √(A/n) to maintain uniform coverage.

Summary Table for Field Area and Sampling

Practical Notes:

• Use **Table

IS 5258: Number Size Distribution - Key Points & Formulas

1. Size Distribution Calculation (Clause 9.1)

• Number of particles in size class ( m_i )
• Mean size of class ( d_i )
• Number of fields examined ( n_+ )
• Area of each field ( a ) (in mm²)

Total sample area: [ A = n_+ \times a ]

Particle concentration in class ( i ): [ N_i = \frac{m_i}{A} \quad (\text{particles/mm}^2) ]

Percentage in class ( i ): [ P_i = \frac{m_i}{\sum m_i} \times 100 ]

2. Worked Example (Table 11, Clause F-1.1.3)

• Shows stepwise calculation of size distribution by number.
• Includes columns for:
  • Size class limits (microns)
  • Sample field area ( a_i )
  • Number of sample fields ( n_i )
  • Total sample area ( n_i \times a_i )
  • Number of particles counted ( m_i )
  • Concentration ( N_i )
  • Percentage ( P_i )
  • Standard error ( S(P_i) = \sqrt{P_i (100 - P_i) / m_i} )

3. Standard Error of Percentage (Column 12)

[ S(P_i) = \sqrt{\frac{P_i (100 - P_i)}{m_i}} ]

4. Procedure Highlights (Appendix G)

• Preliminary scan to estimate number of scans for ~150 particles.
• Adjust scan length if particle count is too low.
• Final counts spread evenly over sample area.
• Total sample area varies per size class.

Summary Table Format (Simplified)

| Size Class (µm) | Sample Field Area (a_i) (mm²) | Number of Fields (n_i) | Total Area (n_i a_i) (mm²) | Particles (m_i) | Concentration (N_i) (particles/mm²) | Percentage (P_i) (%) | Std. Error (S(P_i)) (%) | |-----------------|---------------------------------|-------------------------|------------------------------|

IS 5258: Weight Size Distribution Key Points

1. Weight Size Distribution Formula (Clause 10.3)

The expected standard error ( S(Q_i) ) of the percentage ( Q_i ) by weight in each size class is approximately:

[ S(Q_i) = \sqrt{\frac{Q_i (100 - Q_i)}{n}} ]

• ( Q_i ) = Percentage by weight in size class ( i )
• ( n ) = Number of particles or samples in the class

Note: ( S(Q_i) ) should not exceed 2% for each size class.

2. Conditions (Clause 14.1)

• Standard error ( S(Q_i) < 2% ) for each size class.
• Ensures reliability of size distribution results.

3. Worked Example (Appendix G & Table 11)

• Illustrates step-by-step calculation of size distribution by weight and number.
• Helps verify reproducibility and accuracy.

Summary Table: Expected Standard Error Limit

flowchart TD
    A[Sample Collection] --> B[Sieving into Size Classes]
    B --> C[Weight Measurement of Each Class]
    C --> D[Calculate % Weight \( Q_i \)]
    D --> E[Compute Standard Error \( S(Q_i) \)]
    E --> F{Is \( S(Q_i) \leq 2\% \)?}
    F -- Yes --> G[Accept Distribution]
    F -- No --> H[Increase Sample Size or Reanalyze]

Use IS 5258 Clause 10.3 formula and ensure ( S(Q_i) \leq 2% ) for reliable weight size distribution.

IS 5258 - Reproducibility Key Points

1. Definition & Control Size Class (Clause 14.1.1)

• The control size class is the largest size class containing >5% by weight.
• Denoted by subscript 'o', with mean size ( d_o ), particle count ( m_o ), and sample area ( n_o a_o ).

2. Standard Error of Weight Percentage (Clause 10.3)

• Expected standard error ( S(Q_i) ) of percentage ( Q_i ) in each size class is given approximately by:

[ S(Q_i) \leq 2% ]

• This ensures reliability of size distribution by weight.

3. Reproducibility Requirements (Clause 11 & 13.1)

• Measurements on two or more samples must satisfy reproducibility criteria.
• Standard error of percentage by number in each size class should be < 2%.
• Reproducibility ensures consistency between repeated measurements.

4. Sampling & Counting Procedure (Clause 1.1 & Table 11)

• Preliminary scan: estimate number of scans to count ~150 particles in top 3 classes.
• Analysis: distribute scans evenly; estimate sample area to contain ~25 particles.
• Use Table 11 for illustrative calculation of size distribution by number and standard error.

Summary Table: Standard Error Criterion

Conceptual Flow (Mermaid.js):

flowchart TD
    A[Preliminary Scan] --> B{Count Particles in Top 3 Classes}
    B --> C[Estimate Number of Scans]
    C --> D[Analysis at Lowest Magnification]
    D --> E[Count Particles (~25 per area)]
    E --> F[Calculate Size Distribution & Std Error]
    F --> G{Is Std Error ≤ 2%?}
    G -->|Yes| H[Accept Results]
    G -->|No| I[Increase Sample Size / Recount]

This ensures **reliable, reproducible particle size distribution

IS 5258: Key Formulas, Tables & Specifications for Calculation Procedures

1. Size Distribution by Weight (Clause 1.1)

• Preliminary Scan:
  Scan width = graticule grid width; length = 10-20 mm
  Count particles in top 3 size classes → estimate scans for ~150 particles
  If scans < 5, reduce scan length to get ≥5 scans.

• Analysis at Lowest Magnification:
  Count particles over required scans, estimate total sample area to contain 25 particles.

2. Calculation of Size Distribution by Number (Clause 1.1.3)

Refer Table 11 for a worked example with columns:

3. Combination of Sieve & Microscope Sizing (Clause 1.4, Table 9)

• Use sieve analysis for larger particles and microscope for finer particles.
• Convert sieve sizes to equivalent projected diameters using multiplying factor 0.71 (Appendix A).
• Combine weight undersize and oversize percentages for total sample.

4. Recommended Size Classes (Clause 5.6.2, Table 1)

IS 5258: Control Size Class and Counting Requirements

1. Control Size Class (Clause 13.1.1)

• Defined as the size class with the highest percentage by number of particles.
• Usually the smallest size class.
• If unknown, select the smallest size class present.
• Denoted as:
  • Subscript: o
  • Mean size: d₀
  • Number of particles counted: m₀
  • Sample area: a₀

2. Minimum Number of Particles to be Counted (Clause 14.1.2)

• Minimum particles in control size class: ≥ 25
• If control size class > 10% by weight, count more than 25.
• For standard error < 2%, number of particles m is given by (Clause 10.3):

[ m = \frac{10000}{E^2} ]

where E = allowable standard error (%).

For E = 2%,
[ m = \frac{10000}{2^2} = 2500 ]

3. Size Classes (Clause 4.5)

• Table 1 recommends size class limits based on a base size of 53 microns.
• Size classes increase geometrically (typically by a factor around 1.4).

Summary Table: Control Size Class Parameters

flowchart LR
    A[Start: Identify Size Classes] --> B{Is most frequent size class known?}
    B -- Yes --> C[Select most frequent size class as control size class]
    B -- No --> D[Select smallest size class as control size class]
    C --> E[Count particles in control size class (m₀ ≥ 25)]
    D --> E
    E --> F{Is control size class

IS 5258: Examination Order and Sample Area - Key Points

1. Area of Each Field (Clause 14.1.6 & 13.1.5)

• For control size class, the field area ( a_0 ) = area of the whole rectangular grid of the graticule.
• For other size classes at different magnifications, field area ( a_i ) is adjusted so that: [ n_i \times a_i = n_0 \times a_0 ] where:
  • ( n_i ) = number of fields for size class ( i )
  • ( n_0 ) = number of fields for control size class (minimum 12)
• Ensures constant sample area across size classes.

2. Sample Area (Clause 13.1.3 & 14.1.3)

• Sample area ( A = n \times a ) must be constant for each size class.
• For control size class, sample area may cover the entire slide or multiple slides from the same analysis sample to maintain density consistency.

3. Summary Formula:

[ n_i \times a_i = n_0 \times a_0 \quad \text{with} \quad n_i > 12 ]

4. Practical Notes:

• Use the full graticule grid for control size class.
• Adjust magnification and field size for other classes to keep sample area constant.
• Refer Appendix G for detailed examples.

flowchart LR
    A[Control Size Class]
    B[Field Area \(a_0\)]
    C[Number of Fields \(n_0 \geq 12\)]
    D[Sample Area \(n_0 \times a_0\)]
    E[Other Size Classes]
    F[Field Area \(a_i\)]
    G[Number of Fields \(n_i\)]
    H[Sample Area \(n_i \times a_i = n_0 \times a_0\)]

    A --> B --> D
    C --> D
    E --> F --> H
    G --> H

This ensures uniform particle counting conditions across size classes per IS 5258.

IS 5258: Correlation of Particle Size from Different Methods

Key Points (Clause A-1.2 & A-1.3)

• Particle size varies by method due to shape deviations.
• Sizes from different methods relate via shape factors (multiplying factors).
• Common size methods:
  • Sieve diameter: Nominal sieve aperture size.
  • Projected diameter: Diameter of circle equal to particle's projected area.
  • Stokes diameter: Diameter of sphere with same settling velocity in fluid.

Conversion Factors (Multiply to convert)

Usage Notes (Clause A-1.3)

• Use factors cautiously for extreme shapes (acicular, cleavage planes).
• Prefer experimentally determined factors by overlapping methods or dual sizing of samples.

Example: Combining Sieve & Microscope Sizing (Clause 1.4)

• Use multiplying factor 0.71 to convert projected diameter (microscope) to sieve diameter.
• Combine weight % passing from sieve with projected sizes for full size distribution.

flowchart LR
    A[Sieve Size] -->|Multiply 1.40| B[Projected Size]
    A -->|Multiply 0.94| C[Stokes Size]
    B -->|Multiply 0.71| A
    B -->|Multiply 0.67| C
    C -->|Multiply 1.07| A
    C -->|Multiply 1.50| B

Summary:
Use the above conversion factors to correlate particle sizes from sieve, projected, and Stokes methods, adjusting for particle shape. For unusual shapes, establish specific factors experimentally.