Elif Temiz, 030070195, 8th Week Definitions

1-Allotropic Transformations

New Definition (Better) ( Material Property)

Some crystalline materials can exist in more than one crystal structure in different temperature domains: this phenomenon is called polymorphism of crystalline materials. The polymorphism of metals is called allotropy. Phase transformations from one crystal structure to another are called allotropic transformations. Different crystal structures resulting from allotropic transformations are called allotropic modifications. They are usually marked with Greek letters in the order of their existence as a function of temperature. Allotropic transformation is actually a phase transformation occurring in the solid state. This, similarly to the so-called primary crystallization, a liquid to solid transformation, involves a significant energy change. This is the reason why phase transformations in the solid state, similarly to primary crystallization, result in characteristic break points on the cooling curves of metals. (For example, on the cooling curves of pure metals, a horizontal straight line appears on the cooling curve, indicating a non-variant, constant temperature process.) The non-variant process of allotropic transformation of pure metals can be justified using the well known Gibbs' phase rule. Allotropic transformations are of great significance from the viewpoint of ensuring αgood example of this is the allotropic transformation of tin (Sn). These unfavorable consequences are well known. However, at first people did not assign them to allotropic transformations. Pure tin crystallizes in a body-centered tetragonal crystal structure between 13.2- 161 °C (this is the so-called (3. Sn), which under 13.2 °C is transformed into the α-Sn modification having a lattice similar to the diamond structure. α-Sn - which is called gray tin due to its characteristic gray color - is an extremely brittle phase, while β-Sn, which has a white color, is a ductile and stable modification of Sn. Since β-Sn is extremely stable, the β-> a allotropic transformation spontaneously occurs at a temperature much lower than the equilibrium transformation temperature (T= 13.2 °C). This temperature is lower by approximately 50 - 60 °C. i.e. the phase transformation usually occurs at T=(-30) - (- 40) °C. At the same time, this modification of tin may collapse into gray powder as a result of a minor impact.

 The allotropic transformations of iron are of much greater importance in industrial practice. The allotropic transformations of pure iron, with the indication of transformation temperatures, are illustrated by Figure 4.17. 

Under equilibrium cooling conditions, the crystallization of pure iron from the liquid to the solid state occurs at the temperature T= 1536°C (this is the melting/crystallization point of pure iron). The result of this primary crystallization process is a body-centered cubic crystal called δ. This δ, modification of iron is stable until it reaches the temperature T= 1392 °C. At this temperature, due to the δ->γ phase transformation, the body-centered crystal is transformed into a face-centered cubic crystal (called α). Under equilibrium cooling conditions, at the temperature T= 911 °C the face-centered cubic crystal (γ) will change again to a body-centered modification called α, as a result of γ -> α allotropic transformation.(T he γ-> α phase transformation is extremely important from the viewpoint of heat treatment of practical iron-carbon alloys. This will be analyzed in detail later.)

(Miklós Tisza, Physical Metallurgy for Engineers, pp.102,105)

Previous  Definiton

Materials that can have more than one crystal structure are called allotropic or polymorphic. The term allotropy is normally reserved for this behavior in pure elements, while the term polymorphism is used for compounds. Some materials such as iron and titanium, have more than one crystal structure. At low temperatures, iron has BCC structure, but at higher temperatures, iron transforms to an FCC structure. These transformations result in changes in properties of materials and form the basis for the heat treatment of steels and many other alloys.
(Askeland D.R., Phulé P.P., The Science and Engineering of Materials, pg.62, Kayra Ermutlu)

2-Repeatability

New Definition (Better) (Measurement)

When the transducer is exercised over a set of conditions, and then exactly the same conditions are met again, the difference between the consecutive readings is called repeatability. This is usually tested by maintaining fixed temperature, humidity, and other environmental conditions and then exercising the transducer by changing the measurand between fixed points. For example, the core of an LVDT can be exercised from zero, to full scale, to zero, then to half scale. A data point is taken at the last position. Then the movement of the core is continued to full scale, to zero, then to half scale again. The second data point is taken. This is done repeatedly to obtain a set of data. The standard deviation of this data set is the repeatability.

 It is possible, theoretically, to have a repeatability that has a smaller value than the resolution, by adding noise to the system and making a statistical analysis of the resulting set of data; but this is not helpful to someone using the transducer. So the specified repeatability should not be smaller than the specified resolution. This assures that it is possible for the user to reproduce the specified level of performance. Repeatability can be the most important characteristic of a transducer if the receiving equipment is able to compensate for nonlinearity, temperature effects, calibration error and so on. This is because repeatability is the only transducer characteristic that cannot be compensated. Also, in many control systems, repeatability is more important than transducer accuracy because the system can often be programmed to provide the output desired in response to a given input from the transducer, as long as the input received from the transducer is always the same for a given set of conditions.

(David S. Nyce, Linear Position Sensors: Theory and Application, p.12)

Previous Definiton

Repeatibility (reproducibility) error is caused by inability of a sensor to represent the same value under presumability identical consditions. The repeatability is expressed as a maximum difference between the output readings as determined by two calibrating cycles, unless otherwise specified. It is usually represented as % of FS:

(delta)r=delta/FS*100%

Possible sources of the repeatability error may be thermal noise, build up charge, material plasticit,etc.


(J. Fraden, Handbook of Nodern Sensors: Physics, Design, and Application, p.38)