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Dr. Saad B. H. Farid Particle Size Determination 1 |/ /

Particle Size Determination

A number of Particle Size Determination techniques exist:

1- Size Determination by Sieving Techniques2- Size Determination by Gravitational Sedimentation Techniques3- Size Determination by Microscopy-Based Techniques4- Size Determination by Laser Light Diffraction Techniques

Figure (1): A two-dimensional Fourier transform of a

shape is equivalent to using the shape to produce a

diffraction pattern. a) Some simple shapes used in this

comparison. b) Optical diffraction patterns produced from

the shapes of (a) using a laser and recorded on a

photographic negative. c) Two dimensional Fourier

transforms calculated mathematically from the shapes of

(a)

Figure (2): Calculated Fourier transforms of two differentactual fine-particle profiles, shown with their circle of

equal area imposed over them, demonstrate the effect of

shape on the diffraction pattern. This indicates that caution

should be exercised when using diffractometers to

measure the size distribution of an irregular powder.

Figure (3): The diffraction pattern produced by a set of

round (spherical) profiles can provide information about

the arrangement of the profiles in the array. a) A single

round profile and its diffraction pattern. b) A regular array

of profiles like that of (a) results in a diffraction pattern,which looks like a regular grid of dots of light. c) A

random group of profiles like that of (a) produces a

diffraction pattern similar to that of the single profile.

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Dr. Saad B. H. Farid Particle Size Determination 2 |/ /

Figure (4-a): Optical arrangement of a

typical laser diffraction particle size

analyzer. The several instruments vary

somewhat in their optical configuration

and in the software used to transform the

diffraction pattern data into a size

distribution curve.

Figure (4-b): Schematic Diagram

of Components in a Typical Laser

Diffraction Instrument

Figure (5): Occurrence of Different Particle

Size Measures of a Powder System

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Dr. Saad B. H. Farid Particle Size Determination 3 |/ /

Sources of Error

1.Sampling and specimen preparati on relateda. Errors introduced due to use of non-representative samples, i.e., errors due to incorrect sampling

procedures. This holds true for both dry powders and powders dispersed in suspensions. Proper

sampling procedures can ensure that these errors can be minimized, if not eliminated completely.

b. Analysis of powders finer or coarser than the detection limits of the instrument being used. Evenwhen analyzing powders with dimensions close to the upper and lower detection limits, it is a

good practice to verify the validity of these limits using suitable primary or secondary standards.

c. Errors introduced upon analysis of non-spherical powders. Due to the assumptions of particlesphericity, any deviations from this shape will cause bias and errors to be introduced in the particle

size and size distribution results. Unless analyzed by appropriate algorithms designed as part of

the instrument software, or designed for use on the obtained scattering patterns, it may be expected

that the magnitude or error will be magnified as the deviation from spherical shapes is increased.

d. Errors associated with optical properties of the material. In most instances, it is extremely helpfulto know the optical properties and some physical properties such as density of the material beingtested. Most instruments require the user to provide this information for calculation of the particle

size and size distribution and any errors in these values are reflected in the calculated results.

e. Reliable procedures for creating and maintaining stable dispersions of the powders should bedeveloped. The particles should remain dispersed even in the sample cell, as these instruments

lack the ability to distinguish between primary particles and agglomerates. These procedures

should not cause fragmentation of friable particles or lead to formation of stable bubbles that can

interfere with the measurement and bias the calculated result. Closely related to this is the issue of

sample stability, where certain powders may change size over a period of time due to dissolution

or precipitation mechanisms. In such cases, samples should be prepared immediately prior to

analysis and discarded after analysis.

2.I nstrument and procedure relateda. Errors introduced due to non-aligned or misaligned optics. The need for ensuring proper

alignment has been discussed in detail in the previous sections. Instrument manufacturers specify

procedures and checks to ensure proper alignment.

b. Errors due to lack of background signals or errors in procedures for obtaining backgroundsignals. In this instance, the detector elements use an incorrect background signal to ratio the

diffracted signal. Thus, if the dispersion medium has been changed then an incorrect signal will be

used leading to errors in the calculated size and size distribution.

c. Light leakage due to stray or extraneous lightin the instrument will cause additional signals at thedetector elements that will be analyzed as diffracted signals from the particles and be included in

the size distribution results.d. The use of incorrect optical models will have a significant effect on the calculated size

distributions. These effects may be manifest not only in the range of the size distribution, but alsoin the shape of the distribution.

e. Software related bias may cause significant errors in the calculated results. Most errors wouldarise due to the design of the deconvolution and inversion algorithms that may be based on

assumptions not reflected or applicable to the particle system under study. An example of such an

error would be the use of a model-dependent inversion procedure (i.e., inversion procedure that

assumes a particular shape for the powder distribution) on a multi-modal powder system.

f. Errors due to non-linear detector responses arise when sample loading is either too high or toolow. This issue has been discussed in terms of the obscuration of the incident beam and the need to

ensure obscuration in the range specified by the manufacturer. Put differently, obscuration levels

outside the range specified by the manufacturer correspond to the non-linear response range of the

detector elements, and the current signals generated by the diffracted beam are not proportional to

the diffracted signal incident on the detector.