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ZENER RELAXATION
Mechanical Spectroscopy
LECTURER: 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 10?15
s .
Characteristic Parameters
1)Relaxation strength ΔZ for Zener
2)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, ?2, ∝ ?2 (1 ? ?)2, 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
? ≈ 5.10?14 (???1at C=0.1, (Rb in K) to 530.10?14 (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
times
Arrhenius 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 process
defined 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
Q??1 α[?0f (X0,C) ?2( 1- ?2)/(KT)]  ? (λ(?))2
Type equation here.
where V0 Is the atomic volume
coe?cients ?(p)=(?ε/?χp)σ,T.
Q??1
= ?f (X0,C) ?2
( 1- ?2
)/(KT)]  ? (λ(?)
)2
. ??
?? ? 1+(??)2
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.
Zener relexation p pt
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Zener relexation p pt

  • 1. ZENER RELAXATION Mechanical Spectroscopy LECTURER: PROF. IGOR .S GOLOVIN By: Asad Alamgir Shaikh
  • 2. 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
  • 3. 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).
  • 4. ? 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.
  • 5. 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 10?15 s .
  • 6. Characteristic Parameters 1)Relaxation strength ΔZ for Zener 2)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, ?2, ∝ ?2 (1 ? ?)2, with a Boltzmann factor including the binding energy EB,
  • 7. Cont… ? The relaxation strength varies approximately proportional to 1/T for fixed concentrations. ? For different solid solutions the peak height varies from ? ≈ 5.10?14 (???1at C=0.1, (Rb in K) to 530.10?14 (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.
  • 8. Temperature-dependence of relaxation times Arrhenius 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 process defined by the equation,
  • 9. 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 Q??1 α[?0f (X0,C) ?2( 1- ?2)/(KT)] ? (λ(?))2 Type equation here. where V0 Is the atomic volume coe?cients ?(p)=(?ε/?χp)σ,T. Q??1 = ?f (X0,C) ?2 ( 1- ?2 )/(KT)] ? (λ(?) )2 . ?? ?? ? 1+(??)2 Pair for solute atoms Zener Relaxation.
  • 10. 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.
  • 11. 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.