Since then, magnetostrictive TERFENOLD has been commercially developed as the lanthanide material best suited to drive maximum acoustic power, relatively lowfrequency equipment, including sonar.
TERFENOLD is an intermetallic alloy of the lanthanide elements terbium and dysprosium combined with iron (Fe) and commercially produced as a nearsingle crystal. The name combines the symbols for the elements with NOL, derived from the facility of origin. The material is usually supplied to manufacturers ready to assemble into devices, without the need for further processing.
Design data now available enables the acoustic engineer to choose from the various possible sonar drive materials to produce a design which will best meet system requirements. Certain materials allow electrical and electromagnetic energy to conveniently be transduced (converted) into other forms of energy, such as mechanical energy. Transduction materials generally also show the opposite effect: conversion of incident mechanical energy into electromagnetic energy. While many materials function well as sensors, far fewer efficiently convert input electromagnetic energy into sizeable amounts of mechanical output energy.
Comparing Materials by Coupling Coefficient
The most direct way to compare the various transduction materials is through a parameter symbolised k^{2} the square of the coupling coefficient. k^{2} measures the amount of incident energy transduced into output. To understand the physical origin and meaning of k^{2}, consider the relatively well known analysis of an electrical transformer. The k^{2} parameter is a measure of the mutual coupling between two transformer coils. Here, the amount of magnetic flux generated by a coil of selfinductance L_{1} is related by the mutual inductance (symbolised as M), to the amount of flux threading through or linking a second coil of selfinductance L_{2}. For any two coils, M has the same absolute value regardless of which coil is energised. Through an energy argument, the parameter k^{2} is defined as M_{2}/L_{1}L_{2}, a ratio that represents the amount of an energycoupling ratio. It defines the upper limit of incident electromagnetic energy converted into mechanical output energy. Excluding the inevitable losses, the rest of the incident energy is stored either as an electric field or a magnetic field, both of which can be recovered. If there is no coupling, k^{2} is zero and thermodynamics dictates that the upper limit can never exceed unity.
The strain of magnetostrictive materials tends to be quadratic. That is, regardless of magneticfield polarity, they either constrict with increasing field (nickel) or expand with increasing field (TERFENOLD). Quadratic strain is also a feature of a latemodel ceramic known as PMN, for lead magnesium niobate. (Because strain is quadratic, PMN is correctly categorised as electrostrictive rather than piezoelectric). To maximise equal strain output around a null point, quadratic materials are partially expanded with a static field to the desired null.
This is known as bias. The alternating energy coupled between the two coils by a magnetic field. Using the same derivation method, it can be shown that M is equivalent to intrinsic material property d_{33} through which a bar of transducing material connects an axial electromagnetic field to an axial elastic field. The units of d_{33} are the axial strain in meters per meter divided by the incident field intensity in either amperes per meter or volts per meter. Similarly, L_{1} is equivalent to either the axial electrical permittivity ε_{33}^{T} or magnetic permeability µ_{33}^{T} where elastic stress T is held constant, and L_{2} is equivalent to axial elastic compliance 1/Y_{33}^{X} where incident electromagnetic field X is held constant. Then k^{2} is defined as:
Magnetostrictive
Piezoelectric
The subscript 33 means that cause and effect are both measured along the axial (3) direction.
Parameter k^{2} is sometimes referred to as energy efficiency, but it is really electromagnetic field superposed on the static field then enables positive and negative motion about the null. The common piezoelectric ceramic, PZT, does not need field bias for part of its range, but output can be maximised with bias. TERFENOLD, PZT, and PMN couple more energy per unit volume if mechanical compressive stress bias (prestress) is maximised, with a corresponding electromagneticfield bias. This is because larger stress excursions around null can be accommodated without overcoming the stress bias.
Conveniently, the U.S. Navy has compared very latemodel PZT8 and PMN data with TERFENOLD. These data are reproduced in the table. The table is expressed in coherent MKSA SI units, permitting direct comparison of all electrical, magnetic, and mechanical quantities without need of multiplication factors. For historical context and reference, some properties of Anickel, one of the better nickel magnetostrictive alloys employed in World War II Navy sonars are included in the table.
Thermal properties are from manufacturers’ published data. The Navy reference compares the electromechanical energy density limited both by field and by stress. These values are compared in the table.
Depoling
The tabulated properties do not show that the PZT data are taken near its longlife stress limit. That is, the PZT is not compressed further to avoid losing its performance. Because the piezoelectric phenomenon requires altering the natural crystal symmetry, piezoelectric ceramic performance continuously degrades as it tends to return to its natural state, a process known as depoling. Depoling is accelerated by any combination of overstress, overstrain, overvoltage, or overtemperature. Rates of depoling can be found for various commercial piezoelectric ceramics in manufacturers’ tables. It is assumed that the Navy operates its PZT sonar projectors at the maximum longterm stress limit to maximise energy transduction per unit volume of material and per unit of economical life.
Note that degraded PZT can be repoled to restore performance. As a matter of practicality and convenience, this is not typically done in installed equipment. Magnetostriction of aligned (nearsingle crystal) TERFENOLD is an inherent property, and poling is not required.
Table 1. Comparison of Shape Change Material Properties

Mass Density

kg/m^{3}


8900

7600

7800

9210

Elastic Modulus (Y_{33}^{H})

N/m^{2}


210x10^{9}



29x10^{9}

Elastic Modulus (Y_{33}^{E})

N/m^{2}



74.1x10^{9}

78.7x10^{9}


Permeability (µ_{33}^{T})

Vs/Am


75.4x10^{6}



5.404x10^{6}

Permeability (e_{33}^{T)}

As/Vm



8.854x10^{9}

115.1x10^{9}


Strain Coeff (d_{33})

m/A


6.06x10^{9}



9.10x10^{9}

Strain Coeff (d_{33})

m/V



0.225x10^{9}

0.515x10^{9}


Energy Coupling (k_{33}^{2})



0.012



0.444

Energy Coupling (k_{33}^{2})




0.424

0.181


Prestress

N/m^{2}


7x10^{6}

41x10^{6}

41x10^{6}

41x10^{6}

Alternating Stress (T_{rms})

N/m^{2}


4.95x10^{6}

29x10^{6}

29x10^{6}

29x10^{6}

StressLtd Energy Density

J/m^{3}


117



29000

StressLtd Energy Density

J/m^{3}



11300

10700


Field Bias

A/m





0.1x10^{6}

Field Bias

V/m



0

1x10^{6}


Alternating Field (H_{rms})

A/m


8000



45000

Alternating Field (E_{rms})

V/m



390000

620000


FieldLtd Energy Density

J/m^{3}


494



4912

FieldLtd Energy Density

J/m^{3}



569

7801


Electrical Resistivity



68x10^{9}

>10^{8}

(high)

580x10^{9}

Thermal Conductivity

W/mK


92

~2

~2

13.5

Definitions
µ_{0}=4πx10^{7} VoltSeconds/AmpereMeter is the permeability of free space.
ε0=c^{2}µ0^{1} AmpereSeconds/VoltMeter is the permittivity of free space.
C=299,792,456 meters/second is the speed of light.
Units: A = ampere; kg = kilogram; m = meter; J = joules; K = degrees Kelvin; N = Newton; s = seconds; V = volt; W = watt.
The only known permanent degradation mechanisms of TERFENOLD are melting, which requires temperatures greater than 1200°C, or mechanical shock. If not melted, cooling restores full performance. The limit of destruction is usually determined by the thermal limit of the solenoid coil used to impose the oscillating magnetic field.
Overstrain
TERFENOLD cannot be overstrained. Manufacturers of commercial TERFENOLD sonar claim tens of millions of cycles without measurable change. A Navy prototype TERFENOLD driven projector is reported to have operated over 100 million cycles without failure.
When overstressed, TERFENOLD output merely drops below the design value. Therefore, prestress can be increased beyond the tabulated values, maximizing device energy density. Magnetostriction is significant, near 70 MPa prestress, above which test data is limited. The ultimate tensile stress of piezoelectric ceramics is near that of TERFENOLD, implying no advantage for either material with respect to mechanical shock sensitivity.
Electrical Conductivity and Eddy Currents
TERFENOLD’s electrical conductivity combined with the changing magnetic field it transduces gives rise to eddy currents, which are not a consideration in ceramics. The effect of eddy currents in TERFENOLD is minimised by lamination. The material is sliced parallel to its cylindrical axis (that is, parallel to its strain axis in contrast to a piezoelectric ceramic being cut perpendicular to its strain axis) and then bonded with an insulating epoxy. Recently, wiresaw techniques have been introduced in production, which minimise material loss and cost. It should be noted that all parts of the magnetic circuit must be designed for eddy current control.
Voltage Sensitivity
TERFENOLD is not sensitive to voltage. For piezoelectric ceramic devices to be operated within reasonable voltage limits, the length of an individual element is limited. PZT requires an rms (root mean square) electricfield intensity of about 390 volts per millimeter thickness. (PMN is even higher.) Higher voltage shortens life. Extracting the power potential from PZT requires finite individual element thickness, dictated by electrical safety and practicality, including prevention of corona discharge. Displacement is attained by stacking individual pieces separated by a dielectric material. Stacking and wiring thin wafers imposes manufacturing and reliability problems. The compliance of the epoxy used to bond the wafers absorbs measurable output.
Piezoelectric ceramic electrodes are made of relatively precious materials such as silver and palladium. Inhomogeneous electricfield distribution gives rise to stress concentrations, resulting in microcracks and inactive areas near the electrode ends. Migration of electrode material into the ceramic may exacerbate voltage stress and microcracking.
Permittivity
On the other hand, piezoelectric ceramics exhibit a much higher relative permittivity with respect to free space than does the relative permeability of TERFENOLD with respect to free space. This eases the task of ensuring electricfield uniformity contrasted with the task of ensuring magneticfield uniformity.
Resonant Frequency
Successful design of an electromechanical transducer requires careful attention to dynamic system behavior at different frequencies and often at resonance. Employing a simplified lumped parameter approach, the undamped resonant frequency ƒ_{n} of an elastic bar of shapechange material driving a mass is approximated as the square root of stiffness divided by one third of its uniformly distributed mass plus the driven mass. An undamped system excited at resonance would selfdestruct as energy was added to it with no other place to go. In the real world, there is always damping since all transduction materials operate irreversibly. Each material incorporates various damping mechanisms, which ultimately convert the motion into heat, and reduce the frequency of the theoretical undamped resonance to the realworld damped resonance. Additionally, ceramics inherently are poor conductors of heat. Heat buildup degrades performance, in come cases permanently.
Quality Factor
These dynamic behaviors can be summarised by Q, a parameter called the quality factor. Mechanical Q is a numeric measure of either the mass reactance divided by the damping resistance or, equivalently, it is the stiffness reactance divided by the damping resistance. Mass multiplied by circular frequency is called the mass reactance and assumes the same units as resistance, namely force per unit velocity. Similarly, spring stiffness divided by circular frequency is called the stiffness reactance. A material without losses would have a Q of infinity.
This simplified discussion of Q serves to illustrate its meaning in a purely mechanical dynamic system. There is an equivalent argument for a purely electrical dynamic system. However, in the case of transducing materials, particularly those with high electromechanical k_{2 }coupling ratios, the transducer cannot be viewed in either purely electrical or purely mechanical terms. That is, when operated dynamically, the effects of the mechanical load are evident on the electrical side in the form of impedance changes, and vice versa. It is a common misconception to separate these effects, with consequent difficulties in understanding transducer dynamic behavior. Thus, the output stage of the electrical power amplifier and the load dynamics must be considered as a complete dynamic system during the design process.
Future Development Potential
Piezoelectric ceramics have enjoyed a long period of development funding and ingenuity to reach their near maximum potential as presented in Table 1. By contrast, the nominal properties of TERFENOLD easily compare with the mature ceramics and exceed their development potential. Innovative TERFENOLD transducer designs are still emerging, and full potential of the material has not yet been fully exploited in commercial designs.
Since the initial discovery of lanthanide magnetostriction, improved TERFENOLD materials, design data, and models have become available to designers of sonar and other acoustic devices. Higher volume production and investment in improved manufacturing methods have resulted in a rapid decline in the costs of production TERFENOLD.
Understanding the relative strengths of each material will aid the engineering designer in making the best choices for a given application.
