ZENER RELAXATION

Mechanical SpectroscopyLECTURER: PROF. IGOR .S GOLOVIN

By: Asad Alamgir Shaikh

History Of Zener• During that period from the mid-1930s to the early ’40s,

Zener developed the field of internal friction. • With simple oscillating strain measurements as a function

of temperature, he obtained activation energies for the diffusion of solute atoms in metals, particularly carbon and nitrogen atoms in iron. This development and an associated paper, “A Method of Calculating Energy Losses During Impact” (Zener 1939), led to his call in 1942 to the Watertown Arsenal to develop stronger steel for the U.S. Army

Zener Relaxation

Discovered by Zener in 1943.• A single crystal of α-brass (Cu 70: Zn 30). exhibits a well

defined internal friction peak near 400°C for a Frequency of 620Hz.

• The existence of solute next neighbour pairs or clusters results in a relaxation maximum, called “Zener peak”, in a temperature range where the solute atoms are mobile and enable reorientation of the solute atom pair in the lattice under the action of the applied stress. This applies not only for fcc but also for other crystal types (bcc, hcp).

• Zener estimated the activation energy of the relaxation from the shape of the peak. And obtained a figure of 1.5ev in Cu Zn.

• After that in (1947) he proposed the "pair-reorientation" model which boost up the further experiments and a general interest in the phenomenon.

• Variation of internal friction with temperature in polycrystalline and single-

crystal specimens of α-brass. The measurements were made in torsional

vibration at approximately 0.5 Hz.

Pair-reorientation• There are several atomic

diffusional jumps with unknown consecutive may be involved in each place change reorientation, the pre-exponential jump time in diffusion may not coincide in general with the corresponding value Toz of the zener relaxation, which is in the order of s .

Characteristic Parameters1)Relaxation strength ΔZ for Zener2)Relaxation time τZ show the following dependencies. As pairs of atoms are involved, for dilute and random solid solutions the relaxation strength, which is proportional to the number of reorienting pairs, it should be proportional to the solute concentration squared, , (1 − , with a ∝Boltzmann factor including the binding energy EB,

Cont…• The relaxation strength varies approximately proportional

to 1/T for fixed concentrations.• For different solid solutions the peak height varies from• ≈ 5. (at C=0.1, (Rb in K) to 530. (Cu in Al , C=0.1).• If these values are recalculated per 1 at%, they turn out

to be much lower then for the snoek relaxation, because substitution atoms distort the crystal lattice much weaker then interstitial atoms do.

Temperature-dependence of relaxation timesArrhenius plots of the relaxation times, τ of the Zener peak. Values of τ were determined through the condition, ω τ=1, at the peak position, where ω is the angular frequency. Pre-exponential factors τ0,and activation energies H, for the relaxation processdefined by the equation,

The Zener peak height • In the case of concentrated solid solutions the relaxation

is accompanied by a change of the degree of short-range order. According to the theory of LeClaire and Lomer (1954) the Zener peak height is

Q0f (X0,C)( 1-/(KT)] where V0 Is the atomic volumecoe cients =(∂ffi ε/∂χp)σ,T. Qf (X0,C)( 1-/(KT)] . 1+Pair for solute atoms Zener Relaxation.

Application of Zener relaxation• Zener relaxation for studying the defect-controlled

nature of the atomic mobility in solid solutions probably constitutes its most important application.

References:1) Materials science series [v. 1] A.S. Nowick (Auth.)-Anelastic Relaxation in Crystalline Solids-New York, Academic Press (1972).2) Internal Friction in metallic materials Hand Book.