Particle Size Analysis

• A powder consists of discrete particles with a maximum dimension less than 1000 µm (1 mm).
• Irregularly shaped particle sizes should be expressed as an equivalent spherical diameter due to the lack of a unique dimension.

Direct Dimensional Measurement Methods

• Sieving is applicable for free-flowing dry materials or slurry wet powders within the range of 10-25,000 μm.
• Sieving involves shaking a powdered sample through a series of wires of mesh or aperture arranged in decreasing aperture size.
• Static microscopy enables direct observation (visual or electronic) of irregularly shaped particles.
• Dynamic microscopy involves moving particles-dynamic image analysis.
• Dynamic microscopy captures static images of moving particles for a short duration.
• The period of illumination is determined by the desired magnification, image capture instrumentation, and required resolution.
• Moving particles can be observed through sheath flow systems, electrical sensing zones (ESZ), and free-falling methods.
• Sheath flow systems use a liquid sheath to control particle position, directing the dispersed particle precisely to the image capture instrument's focal point, which allow a still image to be captured through short illumination periods of the flowing particles.
• Electrical sensing zone (ESZ) systems focus image-capture equipment on the orifice in the ESZ tube, where a particle passing through generates an electrical pulse that triggers illumination via a strobe flash at the exact moment of passage, thereby allow capture at the image capture instrument's focal point.
• The free-falling method illuminates particles falling from a vibrating feeder, capturing a still image at the focal point.
• Image analyzers can deduce the area equivalent diameter, the ratio between Martin's and Feret's diameter, or the projected area of each particle in pixels, the perimeter of the particle, the longest dimension, the shortest dimension, and the maximum and minimum Feret diameter.

Transport Measurement

• Gravity is used for particle sizes ranging from 10–1000 µm.
• Centrifugal and ultracentrifugation is used for particle sizes between 0.05–25 µm, which reduces the time involved in sedimentation.

Stoke's Equation

• Used to determine particle size: xs₁ = [18µh/(ps-p₁)t]2, where:
  • h is the height of fall
  • t is the time
  • ps is the density of particles
  • ρL is the density of the dispersed liquid
  • μ is the liquid viscosity

Rapid Physical Response Measurement

• Used for particle sizes between 0.1–1000 μm.
• Methods include electrical sensing zone, light scattering (optical and laser), light diffraction, photon correlation spectroscopy (dynamic light scattering), light blockage, and ultrasonics.
• Electrical sensing zones function based on changes electrical resistance occurring as a particle in an ionic solution passes through an aperture between two electrodes.
• The electrical sensing zone can detect particle sizes from 0.4 - 1200 μm.
• Conductivity changes correlate to the volume of both spherical and irregularly shaped particles passing through its orifice and used to size the particles and count the number of particles passing through the orifice, and determine size, number, volume, and distribution.

Surface Area and Porosity

• Before measuring surface area and porosity, consider physical and chemical adsorption

Physisorption processes (adsorption)

• Due to weak electrostatic or dipole interactions
• Occur between gas molecules and surface atoms (van der Waals and London forces).

Chemisorption Processes

• Due to the formation of chemical bonds between gas molecules and surface atoms involving electron sharing in new molecular orbitals. Also consider incorporation of gas molecules with the substrate, resulting in substrate sputtering.
• The Langmuir isothermal model describes surface interactions under certain conditions such as a uniform adsorbent surface, no interactions between adsorbed molecules, all adsorptions occurring through the same mechanism, and only monolayer formation at the maximum rate. Multilayer absorption is described by BET(Brunauer-Emmett-Teller) isotherm:
• Equation: V = (CBXB)/(VM(1-XB)[1+(CB-1)XB]), where:
  • V is the total volume of adsorbed gas
  • VM is the gas volume in the 1st monolayer
  • xB = P / Psat (gas pressure and saturation vapor pressure at given T)
  • cB = K1 / Km (equilibrium constants for 1st layer and multilayer adsorption)
• Important in characterizing irregular particles by particle size and shape, affecting agglomeration, compaction, and powder technological processes.
• The surface area available for interaction is crucial, especially for internal areas of size-enlarged particles or powders (>1.0 m2/g), determined via low-temperature nitrogen adsorption isotherms and the BET equation to evaluate pore size and shape within particles or voids between particles (not > 500 nm).
• Permeametry, achieved by passing gases slightly above atmospheric pressure through a packed powder bed, evaluates the external particle area
• Porosity, referring to the material matrix within an agglomerated or compacted powder mass, features pores or voids typically ranging from 1.0 nm to 0.1 mm, which are sized by the physical adsorption of various vapours or gases at low temperatures (nitrogen, krypton, carbon dioxide) and ambient temperatures (water, butane, organic vapours).

Mechanical Testing of Elements

Density Measurement

• Pycnometer: Measures density using fluid displacement for solids and fluids.
• Areometer/Densimeter: Measures relative density using a graduated cylinder to probe acidity, anti-freezing agents, and sugar content in grape and wine.
• Westphal's (Mohr's) Balance: Uses hydrostatic weighing with an unequal-arm balance to measure liquid and solid densities.

Hardness Testing

• 1 N (Newton) = 1 kg m / s²
• Normal gravitational acceleration g = 9.80665 m / s²
• 1 kp (kilopond) = 9.80665 N ( 1 kg x 9.80665 m / s² )
• 1 N = 0.102 kp
• Brinell Hardness (HBW): Uses a steel/tungsten carbide ball pressed into the material, suited for coarse but not thin materials; especially uses tungsten carbide with diameters of 1, 2, 2.5, 5, 10 mm and is easily conducted, uses easy and cheap indenters, usable in rough conditions applicable for coarse materials like light metal casting, and estimates the tensile strength for many materials. Some disadvantages include a maximum applicable range of approximately 650 HB, load-dependent Brinell values, limited testing of thin samples, unsuitability for samples with diameters smaller than 1.5 times the ball diameter, and relatively large sample damage.
• Vickers Hardness (HV): Employs a diamond pyramid with a 136° angle for precise measurement. Testing works for very small/thin samples but requires careful preparation. Advantages include ease of conduction, applicability over a broad hardness range, testing capability for very small, thin samples and coatings, as well as minimal imprint, which usually doesn't impair the sample's function. Disadvantages include longer sample preparation times, susceptibility of the diamond indenter to damage, increased liability against vibrations with decreasing applied force, and the impossibility of testing hard-reaching regions (e.g., holes) due to the necessity of using lenses.
• Knoop Hardness (HK): Employs a diamond rhombus with angles of 172.5° and 130° specifically for microhardness tests. Works well for coatings and thin materials, is appropriate for use in harsh working places, applicable in a very broad range of hardness values applicable to very small and can test can test thin samples, as well as coatings tests, and causes minor surface damage. However, it requires very long sample preparation times, is susceptible to damage to the diamond indenter, is liable to increased vibrations liability with decreasing applied force, and involves laborious alignment of the test surface to achieve a symmetric imprint.
• Rockwell Hardness (HRC): Employs either a diamond cone with a 120° angle or a steel ball under applied force. This test is fast and simple but is impacted by surface imperfections; other advantages include easily conducted testing, short testing times, automatable, materials applicability and testing accessibility even in hard to reach materials. Some disadvantages include the possibility of failure through displacement, danger of undetected measurement failures due to indenter damage, and the quality of the diamond having a great influence on the test.

Strength and Elasticity

• Tensile Testing: Measures the force needed to stretch a material, involving 3 deformation and fractures such as double-notched tension, three-point bend, and compact tension.
• Stress-Strain Curve: Demonstrates elasticity (reversible deformation) vs. plasticity (permanent deformation).
• σ = F/A < σs : Stress at breaking point, where
  • σ is stress
  • F is force
  • A is the area
• In ductile specimens (metal or polymer), breaking strength is defined as the stress imposed for the uniform change in the cross-sectional area (Einschnürung) while in brittle materials, that same breaking strength becomes simply the stress at the breaking point.
• Hook's Law: E = σ/ε, where:
  • ε = ΔL/L elongation
  • E is the E-Modul
• Poisson's Ratio: v=-εq/ε, measures a material constant
• Experimentally, stress changes linearly with strain at the beginning. Any deformation in this range is considered elastic and allows the sample to return to its original shape upon stress-removal.
• At higher loads, the stress-strain curve turns nonlinear, describing a plastic deformation, which is a permanent deformation not regressing back to its original state once the stress is relieved.
• The stress at which a permanent deformation sets in defines the elastic limit (or proportional limit), where a 0.2% deviation from such is usually considered to be the onset of plastic deformation.
• Ductility: Ability to stretch without breaking
• For ductile metals, the tensile strength serves as a measure for the maximum load tolerance for a metal under restricted uniaxial loading conditions, where several points may be used: for a typical tensile strength,
  • Point A is the elastic limit;
  • Point A’ is the proportinaly limits
  • Point B can be the yield strength or
• Point C can the offset(Point O to C) yield strength.
• Proportional Limit (A') - the highest stress level at which the stress holds direct proportionality to the strain which must be taken by observation or deviation over a stress-strain curve. Elasticity can be measured by the stress-strain curve with a stress-strain graph. Stress levels are shown at which the strain is proportionate.
• Yield Strength (B) - The stress to produce plastic deformation or in other words, the offset yield strength, and the process to yield it requires that a material be loaded 0.2% over it's yield stength and unloaded so that it remains 0.2% longer.
• Fracture Thoughness measured the resistence by a material to resist crack propagation. Metals: Measured via tensile tests, plus the measurement of both yield strength with elongation.
• Polymers: Show different stress-strain behaviors depending on type

Ceramics

• Tested via flexural (bending) strength or uniaxial compression, with flexure types commonly following either three-point or four-point configurations, where the latter depends on the distance between both points.
• Great compression stems from the strength of the resistance to plastic deformations, and material is insensitive to the compressive strength due to defects as well
• Buckling results if the specimen sample sizes are too long due to the high stresses that make alignment greater with the equivalent strength specimen.
• Nanoindentation: Uses AFM atomic force microscopy.

Radiation And Elementary Particles

• There are four fundamental forces which govern nuclear interactions with matter:
  • Gravitational (Weakest), this act on mass itself
  • Electromagnetism, which acts on charged particles.
  • Strong nuclear binds the components of particle.
  • Weak interacts with radioactive decays.
• Radioactivity can be traced historically to Henri Becquerel(1896) after the discovey.
• Comes from unstable atomic nuclei which stable themselves.
  • E. Rutherford, helped classify this radiation as follows: Alpha, Beta, and Gamma
• Radioactive Half life - Time required for half a radioactive sample to decay.
• unaffected by certain condtions ( temp, pressure, chem state)
• only change via interactions with particles.
• Types of raditions include Alpha beta or gamma: alpha refers to helium nucleus, beta is associated with high penetration and it the emission of decay, and gamma can apply to a few sources such medical imaging or converting a star itself.
• Alpha Radiation has low penetration and has 2n and 2p.
• Beta particles have higher pen than alpa.
• Gamma (y) radiation are photons (E waves) with ME (10²⁰HZ)
• High energy with great pentetration and is unchanged atom or mass wise.
• Used in medical imaging +converting a srta to a hloe with various applications, such as emitting spectroscopcy.
• Nuclear can also capture electrons with a neutrino but it opposes with emission of something similar with beta decays a neutrino will emit a decay as well. Neutron emissions involves the emission of nuclear fission plus reactor and it can measure crystalography.

Radiation Detection Methods

• A Geiger Counter detects radiation through counting. -Proportional counger measures radiation energy .scintillation helps convert luminosity and electrical signsls
• Dosimeter helps personal exposure.

Radiation Applications

Radiation can used medical images or material.

• Nuclear power can harness reactors and Smoke Detector's apply americium to ionize.

This quiz covers the particle size analysis, including methods for measuring particle size, the importance of equivalent spherical diameter, and the use of dynamic microscopy. It also addresses the limitations of image analyzers and the principles behind centrifugal sedimentation.