SIST EN 50324-2:2004

SLOVENSKI SIST EN 50324-2:2004

STANDARD
julij 2004
Piezoelectric properties of ceramic materials and components - Part 2: Methods of
measurement - Low power
ICS 31.140 Referenčna številka
SIST EN 50324-2:2004(en)
©  Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

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EUROPEAN STANDARD EN 50324-2
NORME EUROPÉENNE
EUROPÄISCHE NORM May 2002
ICS 31.140
English version
Piezoelectric properties of ceramic materials and components
Part 2: Methods of measurement -
Low power
Propriétés piézoélectriques des matériaux Piezoelektrische Eigenschaften
et composants en céramique von keramischen Werkstoffen
Partie 2: Méthodes de mesure - und Komponenten
Faible puissance Teil 2: Meßverfahren -
Kleinsignal
This European Standard was approved by CENELEC on 2001-12-01. CENELEC members are bound to
comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.
This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and
notified to the Central Secretariat has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Czech Republic,
Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands,
Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Central Secretariat: rue de Stassart 35, B - 1050 Brussels
© 2002 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 50324-2:2002 E

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EN 50324-2:2002 – 2 –
Foreword
This European Standard was prepared by the CENELEC BTTF 63-2, Advanced technical
ceramics.
The text of the draft was submitted to the formal vote and was approved by CENELEC as
EN 50324-2 on 2001-12-01.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2002-12-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2004-12-01
This part 2 is to be used in conjunction with EN 50324-1.
__________

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– 3 – EN 50324-2:2002
Contents
Page
1 Scope.4
2 Symbols and units.4
3 Dimensions and finish of standard test specimen.5
4 Electrodes .6
5 Environmental requirements .6
6 Small signal data - Timing of measurement .6
7 Number of test specimens.6
8 Methods of measurement.7
9 Determination of a complete set of material parameters -
Systematic procedure.15
10 Errors in calculated coefficients.23
11 Determination of the temperature coefficient of the parameters.24
12 Temperature coefficients of calculated parameters.25
13 Calculation of ageing rates.26

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EN 50324-2:2002 – 4 –
1 Scope
The methods of measurement described in this European Standard are for use with
piezoelectric components produced from the ceramic materials described in EN 50324-1
“Terms and definitions”. Methods of measurement for specific dielectric, piezoelectric and
elastic coefficients are generally applicable to piezoelectric ceramics.
The polycrystalline nature of ceramics, statistical fluctuations in composition and the influence
of the manufacturing process, result in specified material coefficients being typical mean
values. These values are provided for design information only.
Piezoelectric transducers can have widely differing shapes and may be employed in a range of
vibrational modes. Material parameters however, are measured on simple test-pieces (discs,
rods etc. see EN 50324-1, Figure 2) using specific geometric and electrical boundary
conditions. Consequently, the results of the tests provide basic material parameters only and
must only be used as a guide to the actual properties of manufactured commercial
components.
2 Symbols and units
All material constants and equations appearing in this standard are given according to the
International System of Units (SI-units).
Table 1 lists the symbols and, where appropriate, shows the units associated with the physical
quantities designated by the symbols.
Table 1 - List of symbols and their units
Symbol Meaning SI-unit
2
Area
A m
Ageing rate
c See note
2
c Elastic stiffness constant N/m
ij
Capacitance
C F
T
Free capacitance
C F
Diameter
d m
Piezoelectric charge (strain) constant
d C/N or m/V
ij
2
Piezoelectric stress constant
e C/m or N/Vm
ij
Component of the electric field strength
E V/m
i
Measuring field strength
E V/m
m
Frequency
f Hz
Antiresonance frequency (zero reactance)
f Hz
a
Frequency of minimum impedance
f Hz
m
Frequency of maximum impedance
f Hz
n
Parallel resonance frequency
f Hz
p
(maximum resistance)
Resonance frequency
f Hz
r
Motional (series) resonance frequency
f Hz
s
(maximum conductance)
Frequency at first overtone
f Hz
1
Frequency at third overtone
f Hz
3
2
Piezoelectric voltage (stress) constant
g m /C or Vm/N
ij

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– 5 – EN 50324-2:2002
Table 1 - List of symbols and their units (continued)
Symbol Meaning SI-unit
Bessel function of first kind and zero order
J (z)
0
Bessel function of first kind and first order
J (z)
1
Modified Bessel function of first order
J (z)
m
Effective electromechanical coupling factor
k
eff
Transverse coupling factor
k
31
Longitudinal coupling factor
k
33
Shear coupling factor
k
15
Planar coupling factor
k
p
Thickness coupling factor
k
t
Length
l m
Figure of merit
M
Overtone order
n
Frequency constant for thickness mode
N Hz⋅m
t
Frequency constant for radial mode
N Hz⋅m
p
Mechanical quality factor
Q
m
Isolation resistance
R Ω
i
Strain component
S
i
2
Elastic compliance constant
s m /N
ij
Thickness
t m
-1
Temperature coefficient
TC K
2
Stress component
T N/m
i
Dielectric dissipation factor
Tan δ
d
Mechanical dissipation factor
Tan δ
m
Sound velocity
v m/s
Width
w m
Impedance
Z
Ω
Relative frequency spacing
δ
r
Absolute permittivity
ε
ij
Permittivity of free space
ε F/m
o
Temperature
°C
ϑ
Curie temperature
°C
ϑ
C
Phase angle
°
ϕ
3
Density
ρ Mg/m
Resistivity
ρ Ωm
e
E
Planar Poisson's ratio
σ
Angular frequency
rads/sec
ω
NOTE  Ageing rate is commonly expressed as % per decade.
3 Dimensions and finish of standard test specimen
The surface of standard test specimens for characterisation of piezoceramics for transducers
should have an average roughness R < 1 µm before electroding and deviations from flatness
a
and parallelism of the surfaces should not exceed 50 µm per length.
The geometric dimensions of standard test specimens should correspond to the ratios indicated
in Figure 2 of EN 50324-1.

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EN 50324-2:2002 – 6 –
At smaller ratios of the geometric dimensions of the piezoceramic parts, deviations of the
respective vibration modes appear, only allowing imprecise characterisation of the
piezoceramic.
Thickness shear vibrators with rectangular electrode faces have to be polarized in the direction
of the long edge.
4 Electrodes
The electrodes for measurement (and for operation) are deposited by
– firing on of precious metal pastes (e.g. Ag, AgPd, Au),
– electroless plating (e.g. Ni, NiAu),
– vacuum coating: evaporation, sputtering (e.g. Ni, CuNi, Au).
5 Environmental requirements
The electrical measurements shall be carried out at temperatures between 20 °C and 25 °C.
Before each electrical measurement (after electroding), the test specimen must be stored at
these temperatures for at least 24 hours. The test specimen shall be clean and dry.
During measurement, the relative humidity of air in the test laboratory shall be below 65 %.
6 Small signal data - Timing of measurement
The material parameters specified for piezoelectric ceramics (dielectric and electromechanical
properties) require essentially linear relationships between the components of mechanical
stress and strain on the one hand and of electric field strength and displacement or polarization
on the other hand. The material parameters are therefore only valid for a limited range of input
level (under measurement and operating conditions).
The limits of linear behaviour can vary significantly between piezoelectric ceramics of different
composition.
The dielectric and electromechanical parameters of piezoelectric ceramics are subject to a
natural ageing on the basis of the physical phenomenology. Therefore the parameters have to
be measured at a defined time not earlier than 24 h after poling. The parameters have to be
corrected for measurements in longer intervals after poling, bearing in mind the ageing rates
determined according to clause 11.
The parameters of piezoelectric ceramic parts designed as transducers for practical application
should be measured within the second decade of ageing, normally 30 days after poling.
7 Number of test specimens
The characteristic material parameters shall be determined on a minimum of 10 test
specimens.

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– 7 – EN 50324-2:2002
8 Methods of measurement
8.1 Determination of relative permittivity and dielectric dissipation factor
The relative permittivity of piezoceramic materials is determined by measurement of the
capacitance by means of capacitance measuring meters at f = (1 000 ± 200) Hz and
E < 1 V/mm.
m

The dissipation factor tan δ results from the same measuring procedure.
The Curie temperature ϑ results from the maximum of temperature dependent capacitance.
C
This maximum is generally far above the operating temperature range (see 9.2.2 and 11).
8.2 Determination of the electromechanical properties
8.2.1 Dynamic method of measurement
The determination of the electromechanical coupling factors, frequency constants, and the
mechanical quality factor is made in principle by dynamic methods of measurement, that is the
excitation of piezoelectric vibrators to vibration modes at mechanical resonance.
The value of excitation voltages shall be corresponding to a maximum field strength of
0,01 V/mm in general. The dynamic methods of measurement are based on the impedance
diagram (Figure 1) and the admittance diagram respectively of the equivalent circuits of a
piezoelectric resonator.
Reactance X
f
ind.
f f
r a
f
s
Resistance R
Z
m
f
m
f
p
Z
n
f
n
cap.
f
f
Figure 1 - Vector impedance diagram of a piezoceramic transducer
Three pairs of characteristic frequencies which are significant for the specification of the
piezoelectric activity are shown in Figure 1.

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EN 50324-2:2002 – 8 –
The frequencies f , f , f and f , f , f respectively coincide (to a first approximation) for a low-
m s r n p a
loss piezoelectric resonator, that is one with a figure of merit
2
k
eff
M = Q > 20 (1)
m
2
l − k
eff
This is true of all piezoceramics with k > 0,4 and Q > 80 or k > 0,2 and Q > 500 (all
eff m eff m

material groups except type 800) and can be used in the same way for the determination of the
electromechanical coupling factors. Determination of the frequency pair f , f , is only possible
s p
with complex measurements.
The typical characteristics of the measured impedance vs. frequency of a piezoceramic
transducer are shown in Figure 2.
log |Z|
                                                              f
f ≈ f ≈ f f ≈ f ≈ f
m r s n a p
Figure 2 - Measured impedance of a piezoceramic transducer
The use of impedance phase analyzers for the "impedance method" results in the frequency
pair f , f , the frequencies at impedance minimum and maximum and for the "phase method" in
m n
the frequency pair f , f , the frequencies at zero phase angle, ϕ = 0. For practical uses, these
r a
parameters can be approximated with the frequency pair f and f in all piezoceramics except
s p
type 800.
The use of simple ac voltage divider circuits is permissible, when the test specimen is in the
series arm (for f see Figure 3a) or in the shunt arm (for f see Figure 3b), fulfilling the
m n
condition R < |Z| and R > |Z| respectively.
t min l max

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– 9 – EN 50324-2:2002
|Z|
R
o
R
i
a)  f = f
m
G
U
i U
R
t 0
U
R < |Z|
t min
R
l
b)  f = f
n
U
i U
o
|Z|
R > |Z|
l max
Figure 3 - Determination of the frequencies f and f by the impedance method
m n
8.2.2 Determination of electromechanical coupling factors
The electromechanical coupling factors can be calculated directly from the mathematical
relationships of the characteristic frequencies of the respective vibration mode (see 9.2.4.2).
Alternatively, to a first approximation, the electromechanical coupling factors may be
determined from the relative frequency spacing
f − f
p s
δ = (2)
r
f
p
The use of the relative frequency spacing δ corresponds with the determination of the effective
r
electromechanical coupling factor k by the relationship
eff
2 2
ff−
p s
2
k = (3)
eff
2
f
p
This relationship is valid for all vibration modes and supplies the value for the dynamic
electromechanical coupling factor.
The difference in the material coupling factors, which have to be calculated according to the
exact relations, results from the elastic boundary conditions of the various vibration modes.
Material coupling factors (see equations (37) to (44)) are determined graphically from the
effective coupling factor using Figures 4 to 6.

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EN 50324-2:2002 – 10 –
k / k
31 eff
1,113
1,112
1,111
1,11
0,1 0,2 0,3 0,4
k
eff
Figure 4 - Ratio k / k as function of k
31 eff eff
k /k
p eff
1,12
1,1
1,08
1,06
0,1 0,2 0,3 0,4 0,5 0,6 0,7
         k
eff
Figure 5 - Ratio k / k as function of k
p eff eff

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– 11 – EN 50324-2:2002
 k / k
33 eff
 k  / k
t eff
 k / k
15 eff
1,11
1,1
1,09
1,08
1,07
1,06
1,05
0,1 0,2 0,3 0,4 0,5 0,6 0,7
k
eff
Figure 6 - Ratio k / k (also k / k , k / k ) as function of k
33 eff t eff 15 eff eff
For attaining the best precision for the determination of the effective coupling factor of
thickness vibrators, - often full of spurious resonances - the effective electromechanical
coupling factor can be determined from the ratio of the series resonance frequencies of the
overtones to the series resonance frequencies of the fundamentals.
The effective coupling factor k as function of the ratio of the first overtone series resonance
eff
frequency f to the fundamental series resonance frequency f is shown in Figures 7a and 7b.
3 1

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EN 50324-2:2002 – 12 –
k
eff
0,8
0,7
0,6
0,5
0,4
0,3
0,2
3,1 3,3 3,5 3,7 3,9 4,1 4,3
f / f
3 1
Figure 7a - Effective coupling factor k as function of the frequency ratio f / f overview
eff 3 1

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– 13 – EN 50324-2:2002
k
eff
0,55
0,5
0,45
0,4
3,15 3,2 3,25 3,3 3,35 3,4 3,45
f / f
3 1
Figure 7b - Effective coupling factor k as function of the frequency ratio f / f detail
eff 3 1
8.2.3 Determination of the mechanical quality factor
The mechanical quality factor Q is a dimensionless measure of the mechanical losses
m
(reciprocal damping) of a piezoelectric resonator.
...