This is a comprehensive presentation on particle shape. A fundamental property in bulk solids handling. Link to file: https://drive.google.com/open?id=1ilymL-U5rQKhObPO-f5k9-be0FdRkWJ_

1. What is particle shape ?
• Particle shape is the external appearance of a particle.
• Various different aspects of particle shape are of interest and a range of
descriptors has been devised to allow particle shape to be described.
• No single shape descriptor is suitable for all applications.
Particle shape can be described qualitatively using the following descriptors :
• Width/length ratio
• Convexity
• Circularity/roundness
𝑾𝒊𝒅𝒕𝒉/𝒍𝒆𝒏𝒈𝒕𝒉 𝒓𝒂𝒕𝒊𝒐 =
𝒔𝒉𝒐𝒓𝒕𝒆𝒔𝒕 𝒅𝒊𝒂𝒎.
𝒍𝒐𝒏𝒈𝒆𝒔𝒕 𝒅𝒊𝒂𝒎.
=
⊥ 𝒕𝒐 𝒍𝒐𝒏𝒈𝒆𝒔𝒕 𝒅𝒊𝒂𝒎.
𝒍𝒐𝒏𝒈𝒆𝒔𝒕 𝒅𝒊𝒂𝒎.
=
𝑭 𝒎𝒊𝒏
𝑭 𝒎𝒂𝒙
𝑪𝒐𝒏𝒗𝒆𝒙𝒊𝒗𝒊𝒕𝒚 =
𝑨 𝒓𝒆𝒂𝒍
𝑨 𝒄𝒐𝒏𝒗𝒆𝒙
silhouette
𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑫𝒊𝒂𝒎𝒆𝒕𝒆𝒓(𝑫 𝒆𝒒) = 𝟐
𝑨
𝝅
convexivity
Width/length ratio
symmetry
𝑺𝒚𝒎𝒎𝒆𝒕𝒓𝒚 =
1
2
1 + 𝑚𝑖𝑛
𝑟1
𝑟2
Raw Image
Input
Image Analysis
(Object Detection)

2. True Circularity or degree of circularity (Wadell,1933)
𝑫𝒆𝒈𝒓𝒆𝒆 𝒐𝒇 𝒄𝒊𝒓𝒄𝒖𝒍𝒂𝒓𝒊𝒕𝒚 =
𝒄𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒂𝒄𝒆 𝒐𝒇 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒄𝒊𝒓𝒄𝒍𝒆
𝒄𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒇𝒊𝒈𝒖𝒓𝒆
Irregularity(Umbaugh, 2005)
𝑰𝒓𝒓𝒆𝒈𝒖𝒍𝒂𝒓𝒊𝒕𝒚 =
𝟏
𝑪𝒐𝒙′𝒔 𝒄𝒊𝒓𝒄𝒖𝒍𝒂𝒓𝒊𝒕𝒚
Roundness(Wadell,1932)
𝑹𝒐𝒖𝒏𝒅𝒏𝒆𝒔𝒔 =
σ𝒊=𝟎
𝒏 𝒓𝒊
𝑹
𝒏
Where,
ri is the radius of curvature of particle corners
R is the radius of the largest inscribed sphere
n is the number of particle corners measured
Cox’s True Sphericity(1927)
𝑻𝒓𝒖𝒆 𝒔𝒑𝒉𝒆𝒓𝒊𝒄𝒊𝒕𝒚 =
𝒔𝒖𝒓𝒇𝒂𝒄𝒆 𝒂𝒓𝒆𝒂 𝒐𝒇 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒔𝒑𝒉𝒆𝒓𝒆
𝒔𝒖𝒓𝒇𝒂𝒄𝒆 𝒂𝒓𝒆𝒂 𝒐𝒇 𝒕𝒉𝒆 𝒃𝒐𝒅𝒚
“The degree to which the ratio of its volume to its
surface approaches the same ratio for a sphere”
Lappung’s quotient(𝐵𝑒𝑐𝑘𝑚𝑎𝑛𝑛, 1962)
𝑳𝒂𝒑𝒑𝒖𝒏𝒈′
𝒔 𝒒𝒖𝒐𝒕𝒊𝒆𝒏𝒕 =
𝟏
𝑻𝒓𝒖𝒆 𝒄𝒊𝒓𝒄𝒖𝒍𝒂𝒓𝒊𝒕𝒚
(Range : 1-5)
Sphericity and roundness chart
(Cho et, al.,2006)
Fischer’s method of angularity computation (Hawkins,1993)
Power’s scale of roundness(1953)
Cox’s Circularity or classic shape factor (1927)
“The degree to which the ratio of the area to the
circumference approaches the same for circle”
𝑪𝒊𝒓𝒄𝒖𝒍𝒂𝒓𝒊𝒕𝒚 =
𝟒𝝅𝑨
𝒑 𝟐
How to describe it ?
Wadell’s sphericity(1933)
𝑾𝒂𝒅𝒆𝒍𝒍′
𝒔 𝒔𝒑𝒉𝒆𝒓𝒊𝒄𝒊𝒕𝒚
=
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒄𝒊𝒓𝒄𝒍𝒆
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒄𝒊𝒓𝒄𝒖𝒎𝒄𝒊𝒓𝒄𝒍𝒆
=
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒔𝒑𝒉𝒆𝒓𝒆
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒄𝒊𝒓𝒄𝒖𝒎𝒔𝒑𝒉𝒆𝒓𝒆
Tickell’s Sphericity(1931)
𝑻𝒊𝒄𝒌𝒆𝒍𝒍′
𝒔 𝒔𝒑𝒉𝒆𝒓𝒊𝒄𝒊𝒕𝒚 =
𝒂𝒓𝒆𝒂 𝒐𝒇 𝒇𝒊𝒈𝒖𝒓𝒆
𝒂𝒓𝒆𝒂 𝒐𝒇 𝒄𝒊𝒓𝒄𝒖𝒎𝒄𝒊𝒓𝒄𝒍𝒆
=
𝒗𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒃𝒐𝒅𝒚
𝒗𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒄𝒊𝒓𝒄𝒖𝒎𝒔𝒑𝒉𝒆𝒓𝒆

3. • Affects the flow properties
• Powder flow - Spherical particles flow easily
• Liquid flow - Increase in aspect ratio increases viscosity
• Liquid flow - More spherical shape particles lead to low viscosity
• Effects porosity
• Effects friability
• Effects sedimentation rate
• Behavior in sieve analysis
• Powder mixing – blend time changes
• Effects – wall friction, bulk flow properties, abrasivity, adhesion and
cohesion properties.
• Adds more importance to particle size
• Some products work well when :
➢ More spherical – glass beads for highway paint, proppants
➢ Less spherical - abrasives
Unconfined yield
strength of various
shaped particles as
vs consolidation
pressure
Convexity vs
particle size for
various
pharmaceutical
samples
viscosity vs volume fraction
for various shape of
particles
What is it’s significance ?

4. How is it measured ?
FESEM (Field Emission Scanning Electron Microscope)
coated stub stub holder
schematic diagram
coal fly ash
SEM-(Energy Dispersive X-ray Spectroscopy)EDAX
results for fly ash
Principle : High energy field emitted e- are incident in vacuum
on a sample to eject secondary e- , backscattered e- , auger e-
and X-rays. These signals contain information about the
surface morphology and the composition of the sample.
FE-SEMQuanta200
FEG
secondary emission in SEM
Standard : ASTM E3 - 11(2017)
Make/Model : Hitachi - SU3500, SU1510, SU8000; FEI – Quanta
250 FEG; Carl Zeiss - ZEISS Sigma 300, GeminiSEM 500

5. Recent Activities !!!
SEM and EDS/EDAX of Gypsum sample

6. TEM (Transmission Electron Microscope)
TEM
holder
grid
schematic diagram
coal fly ash
Principle : High energy field emitted e- in vacuum
are made to transmit pass through a sample
containing grid to fall on a florescent screen or a
image capturing screen
TECNAI G2 20 S-TWIN
Standard : ASTM F1877 - 16
Make/Model :
Hitachi - HF5000, HF3500,
HF9500, HF9500, HF7800,
HF7700; Carl Zeiss – LIBRA 120
FEI – TECNAI G2 20 S-TWIN;
image system of
TEM
bright vs dark field
imaging
single crystalamorphous polycrystalline crystal
SelectedArea
ElectronDiffraction
(SAED)↴
How is it measured ? Contd …

7. XRD (X-ray diffraction)
PANalytical – Empyrean
Standard : ASTM C1365 - 18
Make/Model : Malvern – Aeris Research Edition,
PANalytical – Empyrean, Empyrean Nano,
Empyrean Alpha 1; Bruker - D2 PHASER, D8
ENDEAVOR, D8 ADVANCE
system schematic
Bragg’s Law : 𝒏𝝀 = 𝟐𝒅 𝒉𝒌𝒍 𝐬𝐢𝐧 𝜽
Where,
n is order
𝜆 is wavelength
𝑑ℎ𝑘𝑙 is the interplaner distance
𝜃 is the angle of maximum diffraction
sample holder powder XRD sample preparation
diffraction peak associated with planes of atoms
Principle : X-ray diffraction is based on constructive interference of
monochromatic X-rays and a crystalline sample. These X-rays are generated by
a cathode ray tube, filtered to produce monochromatic radiation, collimated to
concentrate, and directed toward the sample.
𝑫𝒆𝒃𝒚𝒆 − 𝑺𝒉𝒆𝒂𝒓𝒆𝒓 𝒆𝒒𝒖𝒂𝒕𝒊𝒐𝒏 ∶ 𝝉 =
𝑲𝝀
𝜷 𝐜𝐨𝐬 𝜽
𝑊ℎ𝑒𝑟𝑒,
𝜏 = 𝑚𝑒𝑎𝑛 𝑠𝑖𝑧𝑒 𝑜𝑓 𝑐𝑟𝑦𝑠𝑡𝑎𝑙𝑙𝑖𝑛𝑒 𝑑𝑜𝑚𝑎𝑖𝑛, 𝑤ℎ𝑖𝑐ℎ 𝑚𝑎𝑦𝑏𝑒
𝑠𝑚𝑎𝑙𝑙𝑒𝑟 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑔𝑟𝑎𝑖𝑛 𝑠𝑖𝑧𝑒
𝐾 = 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝑠ℎ𝑎𝑝𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 ~0.9
𝜆 = 𝑋 − 𝑟𝑎𝑦 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
𝛽 = 𝑙𝑖𝑛𝑒 𝑑𝑟𝑜𝑎𝑑𝑛𝑖𝑛𝑔 𝑎𝑡 ℎ𝑎𝑙𝑓 𝑡ℎ𝑒
𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝐹𝑊𝐻𝑀
𝜃 = 𝐵𝑟𝑎𝑔𝑔 𝑎𝑛𝑔𝑙𝑒
How is it measured ? Contd …