Abstract:
An ultrasound resonant spectrometer determines the resonant frequency spectrum of a rectangular parallelepiped sample of a high dissipation material over an expected resonant response frequency range. A sample holder structure grips corners of the sample between piezoelectric drive and receive transducers. Each transducer is mounted on a membrane for only weakly coupling the transducer to the holder structure and operatively contacts a material effective to remove system resonant responses at the transducer from the expected response range. i.e., either a material such as diamond to move the response frequencies above the range or a damping powder to preclude response within the range. A square-law detector amplifier receives the response signal and retransmits the signal on an isolated shield of connecting cabling to remove cabling capacitive effects. The amplifier also provides a substantially frequency independently voltage divider with the receive transducer. The spectrometer is extremely sensitive to enable low amplitude resonance to be detected for use in calculating the elastic constants of the high dissipation sample.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to acoustical measurements in solid materials and, more particularly, to the use of resonant ultrasound spectroscopy to determine a variety of material properties. This invention is the result of a contract with the Department of Energy (Contract No. W-7405-ENG-36). 
     The elastic properties of solid crystals, metals, alloys, ceramics, and glasses are some of the most basic data in the physical sciences. It has long been recognized that these intrinsic properties are related to the acoustic resonances exhibited by solid objects. Acoustic resonance data are also related to defects and sound dissipation properties of the material. 
     I. Ohno, &#34;Free Vibration of a Rectangular Parallelepiped Crystal and its Application to Determination of Elastic Constants of Orthorhombic Crystals,&#34; 24 J. Phys. Earth, pp. 355-379 (1976), incorporated herein by reference, discusses the theory relating resonance frequency data of rectangular parallelepiped crystals to elastic constant determinations. Measurements and numerical algorithms have been obtained for very low dissipation materials where the elastic constants are already known to within a few percent or better. 
     In a conventional resonance measuring system, described by Ohno, a rectangular parallelepiped specimen is placed between two piezoelectric transducers. One of the transducers is excited by a sweep frequency synthesizer and the output signal from the other transducer is amplified and displayed as a function of exciting frequency. A spectrum of the sequence of resonance response peaks from the sample is determined for analysis. The specimen is placed in contact with the transducers on its corners as lightly as possible to preclude suppressing resonance peaks while avoiding resonance frequency shifts under increased specimen loading. 
     There are some problems with conventional resonance measuring systems which significantly impact the application to crystalline materials. Two of the problems are identified by T. Goto et al., &#34;An Apparatus for Measuring Elastic Constants of Single Crystals by a Resonance Technique Up to 1,825K,&#34; unpublished (1978). When the transducer is in direct contact with the specimen, many normal vibrational frequencies of the transducer itself are superimposed on the resonant modes of the specimen. Goto did not detect this problem in the high temperature device described in the article, wherein buffer rods transmit the specimen response to remotely located transducers, because the sample resonances were very sharp. The resonant frequency shift, mentioned above, is also noted, along with a mention that the applied load cannot become too close to zero because some of the vibrational signals of the specimen would become too small to be detected. The solution was to maintain a 5 g load on the specimen. 
     These conditions have made the conventional procedures difficult to apply to high dissipation materials, such as some glasses, high temperature superconductors, composites, and also materials generally at temperatures below 100K, etc. For low dissipation materials, the transducer can be damped by bonding the transducers to high dissipation solids whereby the sample response amplitudes are sufficiently greater than spurious resonant responses from the mechanical system that the specimen responses can be readily distinguished. For higher dissipation materials, the spurious resonances have amplitudes as large as the sample response amplitudes. These extra frequencies make the numerical analysis difficult to implement. Beat frequencies also occur, destroying the shape of the sample resonances. 
     Further, highly dissipative materials (low Q) produce weak signals. Conventional detectors, i.e., diode detectors, introduce a dead zone for signals having a strength below 0.6 V, obscuring the response shapes. Merely increasing the drive level introduces further inaccuracies from non-linear and heating effects. The problem of weak signals is compounded by the capacitive nature of the transducers. Conventional amplifiers have an input impedance which, in combination with the impedance of the transducer and connecting cable, provides an RC rolloff in the frequency range of interest to produce a strongly frequency dependent system gain, obscuring the low frequency resonances. 
     These and other problems of the prior art are addressed by the present invention and an improved resonance spectrometer is provided which can be used with high dissipation materials. Accordingly, it is an object of the present invention to enable the measurement of resonant frequencies of high dissipation materials. 
     It is another object of the present invention to provide a transducer which is mounted to substantially eliminate system resonant response signals at frequencies within the expected sample resonance range. 
     One other object of the present invention is to minimize input signal losses to the signal amplifier. 
     Yet another object of the present invention is to produce accurate representations of sample resonance shapes. 
     Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
     SUMMARY OF INVENTION 
     To achieve the foregoing and other objects, and in accordance with the purposes of the present invention, as embodied and broadly described herein, the apparatus of this invention may comprise an ultrasound resonant spectrometer for use with a rectangular parallelepiped sample of a high dissipation material having an expected resonant response frequency range. A sample holder structure contacts corner portions of the sample with a drive transducer assembly and a receive transducer assembly mounted on the sample holder. The receive and drive transducer assemblies derive an output response of the sample from the receive transducer assembly as the drive transducer assembly excites the sample over the expected resonant response frequency range. A transducer is mounted on a thin membrane for weakly coupling the transducer to the sample holder structure. The transducer further operatively contacts a material effective to substantially remove system resonant responses at the transducer within the sample resonant response frequency range. A square-law detector amplifier amplifies the response signal output from the receive transducer while preserving the signal shape. A cable having a center signal conductor, a first shield isolated from ground, and a surrounding grounded second shield connects the receive transducer assembly with the amplifier. The amplifier includes a unity gain section for driving the isolated shield with a signal matching the signal on the signal conductor effective to eliminate capacitance effects from the cable and minimize signal loss. 
     In another aspect of the invention, an improved transducer assembly is provided for the receive and drive transducer assemblies in a resonant ultrasound spectroscopy system having a sample holder structure for contacting corner portions of a rectangular parallelepiped sample of a high dissipation material, where the receive transducer assembly and a drive transducer assembly contact the sample. The transducer assemblies include a transducer mounted on a thin membrane for weakly coupling the transducer to the sample holder structure. The transducer further operatively contacts a material effective to substantially remove system resonant responses at the transducer within the sample resonant response frequency range. 
     In yet another aspect of the present invention an amplifier, for use in an ultrasound resonant spectroscopy system having a sample holder structure with a drive transducer and a receive transducer for contacting corners of a rectangular parallelepiped sample for transmitting sample responses up to about 4 MHz, minimizes signal losses from the receive transducer and preserves the sample resonant response shape. The amplifier has a unity gain input amplifier for driving an isolated shield surrounding the signal conductor in a cable connecting the receive transducer to the amplifier with a signal matching the sample response signal on the signal conductor to effectively eliminate capacitance effects from the cable transmission. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and form a part of the specification, illustrate embodiments of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings: 
     FIG. 1 is a schematic drawing in block diagram format of an ultrasound resonant spectrometer according to the present invention. 
     FIG. 2 is a schematic drawing of a low-noise detector for use in the system shown in FIG. 1. 
     FIG. 3 is a pictorial illustration, in partial cross-section, of a transducer assembly for sample mounting. 
     FIG. 4 is a cross-sectional view of one embodiment of a transducer according to the present invention. 
     FIG. 5 is a cross-sectional view of a second embodiment of a transducer according to the present invention. 
     FIG. 6A is a response graph from La 2  CuO 4  from 0.5-2.0 MHz. 
     FIG. 6B is a response graph from La 2  CuO 4  from 2.0-3.0 MHz. 
     FIG. 7 is a flow diagram for determining elastic constants from resonant response data. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to FIG. 1, there is shown a schematic drawing of an ultrasound resonant spectrometer according to one embodiment of the present invention. Sample cell 10 includes drive transducer assembly 12 and receive transducer assembly 14 for receiving and holding a material sample therebetween for ultrasound resonant spectroscopy. Low frequency oscillator 16 generates a modulating output 18 for input to frequency synthesizer 22 to cause synthesizer 22 to generate a sweeping range of output frequencies 24 for input to drive transducer assembly 12. Transducer assembly 12 includes a transducer, typically a piezoelectric crystal, for vibrating a sample material (e.g., sample 62 in FIG. 3). As drive frequency 24 sweeps through frequencies which are resonant with a sample, an enhanced output 30 is produced by receive transducer assembly 14. 
     Output signal 30 is passed along a conductor 32 to low noise detector 38 for generating square-law output signal 44. Detector 38, more particularly described with reference to FIG. 2, provides an input impedance which has a very high resistance and a low capacitance to form a voltage divider with the transducer capacitance which is frequency independent. If the detector input capacitance is lower than the capacitance of the transducer, the voltage divider ratio can be made close to unity. The frequency-independent voltage divider preserves the shapes and relationships of the sample resonant responses. 
     It will also be appreciated that the capacitance of the connecting cable 28 can significantly attenuate the strength of the signal 30 reaching detector 38. For example, a coaxial cable of length 2 meters may have a capacitance of 200 pF, providing an attenuation factor of about 25 dB for typical output signals from a receive transducer with a capacitance of about 10 pF. In accordance with the present invention, cable 28 includes center signal conductor 32, isolated shield 34, and grounded shield 36. Detector 38 further includes a unity gain input amplifier which outputs signal 42 to isolated shield 34. Signal 42 matches signal 30 on center conductor 32 to minimize the voltage difference between conductor 32 and shield 34, thereby eliminating the capacitance therebetween. 
     Signal 44 is output from detector 38 for input to digital voltmeter 46 to produce a digital output signal 52 for input to computer 54. A thermocouple signal 48 may also be output from sample cell 10 for use in processing the response data 44. Digital resonance signal 52 is input with synthesizer 22 output frequency signal 26 to computer 54 for developing a resonant response spectrum from the material sample. Computer 54 may also include software for processing the resonant spectrum to derive the material constants, i.e., the elastic constants, for the sample. The system shown in FIG. 1 produces an output signal 44 having a lorentzian shape with resonant responses limited to those of the material sample from which the elastic constants can be deduced. 
     A schematic diagram of a low-noise square-law detector for use in the ultrasound resonant spectroscopy system of FIG. 1 is shown in FIG. 2. The detector includes a unity gain input stage (components Q1-Q9) for inputting transducer signal on conductor 32 and outputting a matching signal 42 on isolated shield 34, operational amplifier stages (U1-U3), a communications demodulator (U7) having square-law output, and an instrumentation amplifier (U4a,b,c) with unity gain low-pass filter (U4d) to generate the analog output square-law signal 44. Circuits U5 and U6 provide the voltage supplies for demodulator U7. 
     In the unity gain amplifier stage, transistors Q8a and Q8b may be a matched JFET pair on a single substrate. Transistor Q8b has the source biased one diode drop voltage above the negative power supply (-15V) by the configuration of transistor Q4, and its gate is at the negative power supply voltage. Thus, transistor Q8b acts as a constant current source. The drain of transistor Q8b is driven at a constant voltage by transistor Q2, which is connected as an emitter-follower. Transistor Q2 is biased with the emitter one diode drop below the base and the base is one diode drop plus 5.0V above the negative power supply due to transistor Q1 and zener diode D1. This voltage is held constant and no RF is present whereby parasitic capacitance does not degrade performance. The current through transistor Q2, and therefore Q8a and Q6 is constant and equal to the current determined by the gate-source voltage of transistor Q8b. 
     Because of the constant current through transistor Q8a, the gate-source voltage is held at one diode drop. The signal input from signal conductor 32 is connected to the gate of transistor Q8a and sees the capacitance of transistor Q8a and static protection diodes D3, D4 (about 1.5 pF) and the practically infinite resistance of the transistor Q8a gate. Thus, the input characteristics provide the required capacitive voltage divider with the transducer which is independent of the frequency. The source voltage of transistor Q8a is one diode drop below the gate and tracks the input voltage exactly, providing a voltage follower, or unity gain, stage. The output from transistor Q8a source is input to current amplifier transistor Q3, connected as an emitter follower to provide the output signal at the emitter at a higher current. 
     Parasitic capacitance effects are eliminated by the action of transistors Q6, Q9, and zener diode D2 to maintain a constant drain-source voltage of 5.0V plus one diode drop across Q8a. Transistors Q4 and Q5 maintain a constant current through transistor Q7 equal to the current through transistor Q8a to fix the drain-source voltage of transistor Q7. Thus, transistor Q7 acts as a dynamic load for the output. 
     The output signal from transistor Q3 is output 42 to the isolated shield 34 of cable 28 (see FIG. 1) and also to unity-gain, operational amplifier buffer U1. Amplifier U1 then drives gain stages U2 and U3. In one embodiment, amplifiers U1, U2, U3 provide a voltage gain of 100 and a bandwidth of about 10 MHz. The amplified output is input to demodulator U7 which provides outputs at pins 6 and 12 which are the square of the inputs at pins 1 and 4, but out of phase with each other and 10.5V above ground. Amplifiers U4a,b,c form a conventional instrumentation amplifier which shifts the outputs of demodulator U7 to ground and subtracts the out-of-phase signal to produce a doubled output of the squared input referenced to ground. Amplifier U4d is connected to form a unity-gain, low-pass filter to remove the frequency-doubled component produced by demodulator U7. Output signal 44 is a dc signal exactly proportional to the square of the amplitude of the rf input signal 30 on conductor 32 at transistor Q8a. Output signal 44 is insensitive to phase and has a very low noise. 
     Preferred components for the circuit depicted in FIG. 2 are as follows: 
     
         ______________________________________D1, D2     1N751A      Q1-Q6     2N2857U1-U3      LM6361      Q2        2N4416U4         LM224       Q8        2N3954AU5         7812        Q9        2N3251AU6         7905U7         MC1596G______________________________________ 
    
     Referring now to FIG. 3, there is shown, in partial cross-section, sample cell 10 for operation in a simple helium flow cryostat from 9K to 350K. Drive transducer assembly 12 is mounted within cell 10 and is electrically connected with sweeping output frequency signal 24 to drive material sample 62. Receive transducer assembly 14 is mounted on hinged arm 64, which pivots on needle bearing 66. The force applied to sample 62 is solely from the weight of arm 64 rather than springs, thereby enabling stable resonant frequencies from sample 62 as the temperature is varied. Loading screw 68 provides for adjustment during loading of the sample 62. The output signal from receive transducer 14 is transmitted through triaxial cable 28 along center conductor 32, with isolated shield 34 and grounded shield 36 for removing capacitance effects. Thermocouple 72 transmits temperature data signal 48. The transducer assemblies 12, 14 are shielded by rf shield 74 and copper shields 76 and insulation 78 reduce heat leaks to sample cell 10. 
     The design of transducer assemblies 12, 14, in accordance with the present invention, substantially removes any transducer response to system resonances within the expected range of sample resonances. This is particularly necessary for receive transducer assembly 14. In the FIG. 4 embodiment, the resonant frequency of the transducer assembly is increased beyond the expected sample resonance range. In the FIG. 5 embodiment, the transducer assembly is damped for resonant frequencies in the sample resonance range. In both cases, transducers 82, 102 are bonded, e.g., with Stycast 1266 epoxy, to flexible membranes 86, 106, which may be a 0.001 inch thick membrane of DuPont Kapton H-Film, which has been coated on one side with evaporated silver for electrical contact and rf shielding. Membranes 86, 106 are thin enough to prevent acoustic coupling between transducers 82, 102 and the mounting shells 84, 104, eliminating any transmission of cell 10 (FIG. 3) resonances. Transducers 82, 102 are electrically connected using ribbons 94, 112, which may be strips of 0.001 inch thick, 0.040 inch wide DuPont Kapton coated with a conductive material, such as silver. Coated ribbons 94, 112 have a low self-inductance and low mass to preclude self-induced electrical or mechanical resonances which can be associated with thin wires. 
     Referring now to FIG. 4, transducer 82 is mounted below a cylinder 92 of material having a sound velocity much higher than the sample material in order to remove any system resonant response from the expected sample resonant responses. A material such as diamond (17 kM/s speed of sound) or beryllium (12 kM/s speed of sound) may be used. A diamond cylinder of 1.5 mm diameter and 1.0 mm length and bonded to membrane 86 has a lowest resonance at about 4 MHz and is a preferred material. Membrane 86 has an opening below transducer 82 to permit transducer 82 to contact a sample directly. The bonded cylinder approach has a very flat frequency response. 
     FIG. 5 shows a damped transducer 102 with a damping powder 114 filling mounting shell 104 above transducer 102. A powder 114 of 1 micron PbO has successfully damped frequencies above 1.2 MHz. The powder is held in place with a thin tissue cover 116. A suitable transducer, e.g., a 1.5 mm diameter lithium niobate transducer, has bending mode resonances which occur below 3 MHz which are, therefore, damped by powder 114. As shown in FIG. 4, membrane 106 also has an opening below transducer 102 to allow transducer 102 to contact the sample directly. It should be noted that the damped arrangement only reduces the amplitude of unwanted resonances, but the resulting very weak, broad resonances might still affect the output signal for very small sample signals and the diamond cylinder approach would be preferred in such instances. 
     FIGS. 6A and 6B are response graphs from a small single crystal of La 2  CuO 4 , a high dissipation, low Q material, using the apparatus of the present invention. The sensitivity of the apparatus is apparent from the number of small resonant responses detected by the apparatus, e.g., at about 1.3 MHz, 1.5 MHz, 2.1 MHz, 2.3 MHz, etc. All nine independent elastic constants were able to be determined from the response data using the analysis method hereinbelow discussed. 
     A flow diagram for deriving elastic constants from natural resonant response data is shown in FIG. 7. A program listing for implementing the flow diagram is provided in the appendix hereto. As developed by the Ohno publication, supra, it is straightforward to compute frequencies from elastic constants. Thus, the basic procedure of the process shown in FIG. 7 is to form a first estimate of the elastic constants, compute the expected resonant responses, compare the calculated response with the measured response, adjust the elastic constants, and repeat the process until a minimum difference exists. 
     The measured resonant response frequencies are input 102 to the program. Sample characteristics of density and dimensions, and an initial set of elastic constants determined from available sources, are input 104 to subroutine &#34;Ohno&#34; 106 for computing a resonant frequency spectrum from the trial parameters. A figure of merit F is computed 108 from the differences between the calculated and measured resonant response frequencies. The function F may be as simple as a sum of the squares or a more elaborate sum of Gaussians or Lorentzians. 
     The elastic constant space is then searched for the minimum of F using a minimization scheme, e.g., a conjugate-gradient algorithm such as provided by ZXCGS available from IMSL, Houston, Tex. The convergence criterion employed by ZXCGS is that the sum of the squares of the derivatives of F with respect to the independent variables, the elastic constants, becomes less than some predetermined number. If the data are converged 112, i.e., a minimum has been attained, the calculated elastic constants are output 124. It should be noted that the formation of F requires the assumption that there is a one-to-one correspondence between the measured and calculated resonance lines and that there are no missing or spurious resonance lines. 
     If F is not yet a minimum, the routine determines if F is progressing toward a minimum 114. If not, the routine ends 116 so a new set of trial parameters can be entered. Otherwise, the interim results 108 are used to improve the estimates for the elastic constants 118. The revised constants are then input to subroutine Ohno 122 for calculating a new set of resonant frequencies and a new figure of merit F is computed 108. The process is repeated until the routine determines that F has converged 112 on a set of elastic constants. If one set of elastic constants is determined at one temperature, that set can form the trial elastic constants for finding the constants at nearby temperatures to reduce the time for convergence. 
     Thus, a transducer assembly has been provided which does not introduce spurious resonances within the expected range of sample resonances. In one embodiment, transducer resonant frequencies and concomitant resonant responses are removed from the sample range and, in another embodiment, the transducer resonant responses are removed by damping. The transducer is weakly coupled to the sample cell assembly by a flexible membrane whereby apparatus resonances are not transmitted to the transducer. The resonant frequency responses of the sample can be clearly resolved for use in determining the sample characteristics of interest. 
     The foregoing description of the preferred embodiments of the invention have been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto. ##SPC1##