Ti 3 Al C 2 example essay topic

This paper provides an introduction to the technology and procedures pertinent to calculate the transit time of a ultrasonic wave in a solid state material. The technique is applied to two types of layered ternary carbides. I. Introduction Methods that employ the use of ultrasonic sound waves permits us to! SS see through!" opaque materials. As early as the 19th century, people in many different fields utilized the information provided by an object's resonance.

During the industrial revolution, comparing the resonance of manufactured parts improved the steel smelting process [1]. The timbre from a musical instrument is depended on the quality of the material used to make it [2]. In the field of physics, the resonance spectra of any solid state material is depended upon the physical composition [3]. The benefit of using ultrasonic techniques is that it offers a nondestructive method in researching structural integrity.

The goal of this report is show how to determine transit times of ultrasound waves in a solid state material. This will include a description of the echo pulse generation and detection device, sample set-up, determining transit times, and how to calculate the elastic properties and Debye temperature using the velocities of the sound waves. Also included, is an analysis of two types of layered ternary carbides: Ti 3 Al C 2 and V 2 Al C. II. Experimental Details Ram-10000-0.2-17.5 The Ram-10000 system is used in this study to generate and measure the transit times of the ultrasonic waves. This system uses superheterodyne circuitry to that found in standard radio receivers or lock-in amplifiers. The modulating driving signal is produce by using the analog multiply number one to multiply the reference output of the intermediate frequency (IF) (1) by the output of the high frequency synthesizer (2).

(1) (2) Where AIF and As are the amplitudes of the IF oscillator and synthesizer outputs, F represents the ultrasonic frequency, t is the time, and f"OIF and f"Os refer to the arbitrary phases. The product of the two produces the operating frequency plus a high frequency component. (3) The low-pass filter removes the high frequency term and the cosine term containing the sum of the frequencies. Then the difference term is applied to the gated amplifier. This creates the high power RF burst required to drive the transducer. The superheterodyne receiver is equipped with a pair of phase-sensitive detectors, which process the received ultrasonic wave.

The received signal can be represented by, (4) where Fr and f"Or represents the frequency and phase of the received signal. The signal is first amplified then multiplied by the synthesizer output in Mult. No. 2, the voltage will look like, (5) where g 2 contains the RF gain, the amplitude of the reference, the conversion efficiency of the multiplier. The higher frequency term along with the cosine term containing (IF+F+Fr) are rejected by the IF amplifier. The Ram-10000 has a fixed center frequency of 25 MHz and three others band widths that can be selected using the provided software: 0.4 MHz, 1 MHz, and 4 MHz.

The signal is once again amplified and then multiplied by the IF oscillating output multipliers number 3 and 4. (6) (7) Equations 5, 6, and 7 represent the quadrature phase-sensitive detection process. Transducers The most important part of an ultrasonic measurement system is the transducer. The transducer converts the electrical energy from the RF burst to mechanical energy (transmitter mode) and mechanical energy into electrical energy (receiver mode). In this study we used quartz piezoelectric transducers. According to the manner in which the piezoelectric crystal is cut, it vibrates in the direction of the thickness producing longitudinal!

SScompression!" waves or in the tangential direction producing shear waves. The pulse from the transducer has a characteristic bell shape frequency spectrum with maximum near the natural frequency of the piezoelectric element, which depends on its thickness [4]. Experimental Setup The setup to run this experiment is fairly straightforward. First, the sample must have polished parallel sides. The measurements in this study are dependent upon the clarity of the received signal. Uneven sides will make it hard to determine one echo from another.

The oscilloscope should show separation between the echoes much like the image in figure one. The transducer in this experiment was bonded to the sample using a phenyl salicylate know as Salol. This bonding agent provides good coupling of the acoustic waves at room temperature. If the experiment requires wider range of temperatures, there are other bonding agents that could be used at specified temperature ranges [5]. Figure 2 shows a very general block diagram of the experimental setup.

The generated pulse leaves the RAM-10000 through the diplexer to the transducer. The transducer converts the electrical energy to mechanical energy, which produces an ultrasonic wave. The wave then reflects off the opposite side of the sample and proceeds back to the transducer, which converts the acoustical energy to electrical energy. The signal passes through the diplexer back to the RAM-10000. The diplexer protects the receiver-preamplifier circuitry from being damage from any high voltage signals coming from the transducer.

The RAM-10000's superheterodyne quadrate phase sensitive detection circuitry analyzes the received signal, as described above, and sends this information to the oscilloscope and the data acquisition board (D.A. B). The oscilloscope displays the echo pulse pattern detected by the RAM-10000 (pictured in fig. 1). The DAB sends the information about the signal to the computer, where the data is stored. All controllable functions are link to the RAM-10000 by the D.A.B. In this experiment we want to record the transit time as function of the material's temperature. The RAM-10000 is equipped with an external monitor input.

This will allow continuous recording of the temperature change during the duration of the experiment. We will insert the sample housing into a cryostat filled with liquid nitrogen. The heater connected to the temperature controller will help in controlling the rate in which the sample warms and cools. Figure 3 is a diagram that represents the sample holder. Transit Time The measurement system can measure the transit time of the echo produced by the ultrasonic wave. First, the sample must be mounted on the holder.

Then the integrator gate's width and delay can set so that the integrator contains the echo. To calculate the transit time, two of the echoes must be integrated. Figure 1 shows the segment that defines the time difference. The integrator outputs are expressed as: (8) (9) where t 1 and t 2 are time intervals defined by the integrator gate. The phase angle of the received signal can be calculated by the arc tangent of the quotient of the two integrator outputs: (10) The time of flight of the sound through one thickness of the sample can now be expressed as: (11) where N 2 and N 1 are the echo numbers. Elasticity The expression that describes how an object responds to stress is the well-known Hooke's Law.

Hooke's Law can be formatted into a tensor using this formula: (12) where f~air is the applied stress, c is the elastic constant, and f'eij is the resulting strain [6]. The longitudinal and shear velocities in a solid state material can be calculated using the following relations: (13) (14) where C 11 and C 44 are the elastic and shear modulus and f^afn is the sample's density. The mean integrated velocity can be expressed as: (15) The elastic constant can be calculated from: (16) (17) (18) where E and f'Yfnare the Young's and shear modulus and f'efnis the Poisson's ration. Elastics are bulk thermodynamic property just like thermal expansion and specific heat [6]. In this study we are also interested in the Debye temperature of the sample. In Debye theory, the Debye temperature is the highest temperature that can be achieved in a crystal due to a single normal vibration [7].

The Debye temperature is given by: (19) where h is Planck's constant, k is Boltzmann's constant, and N is the number of atoms per unit volume. This express can be used to solve for the heat capacity of a material. In this paper we will not calculate the heat capacity. fn II. Results and Discussion To determine the accuracy of the experimental setup we used the layered ternary carbide Ti 3 Al C 2. We compared the results we measured with previous papers that employed the same experimental technique [5, 7]. To offer a comparison with another material, we measured another layered ternary carbide, V 2 Al C [8].

Layered Ternary Carbides Layered Ternary Carbides can be represented by the formula, Mn+1 An, where n must be greater than 1, M represents an early transition metal, A is an A-group element, and X is either carbon or nitrogen. The structure of these compounds consist of tightly pack transition layers of carbide or nitride that are interleaved with layers of A. These compounds are good thermal and electrical conductors, damage tolerant, and are resistant to thermal shock. Their Vickers Hardness values are between 2 and 4 GPA, which means that they are machinable [5, 7, 8]. Some of the physical and measured properties of these two carbides that were used in this experiment can be found in table 1.

Table 1 Measure and Physical Properties Ti 2 Al C 2 V 2 Al C Density! SSf^a!" g / cm ^3 4.5 4.6 Length! SSl!" mm a 10.97 9.88 b Thermal Expansion Coefficients! SSf~N!" K^-1 9.1 x 10^-6 8.3 x 10^-6 Number of Atoms Per Unit Volume atoms / angstroms ^3 3.171 x 10^-1 2.195 x 10^-1 a. the length represents the distance traveled by the sound wave at room temperature b. due irregular shape of this sample the length was an average of three measured lengths Experimental Method The purpose of this experiment is to calculate the Young's and shear modulus, Poisson ratio, and the Debye temperature.

To do this we needed to find the longitudinal! SScompression!" and shear velocities in the two samples. First, we applied the longitudinal transducer to the sample as described above and took an absolute transit time measurement. The operational settings for this procedure can found in table 2. The oscilloscope displayed the waveform that represented the echo pattern in the sample. By using the display we were able to position the integrators in the correct time intervals to analyze the first and second echoes.

The absolute measurement was taking at room temperature. Next, the sample is place into cryogenic chamber filled with liquid nitrogen. At this time the RAM-10000 is set to measure the relative change in transit time. To minimize the amount error the RAM-10000 can be set to average a specified amount of readings.

The same procedure was used to calculate the shear velocities. Table 2 Operational Settings Longitudinal Transducer Shear Transducer Operating Frequency MHz 9.9 5 Cycles Per Burst 8 8 Burst Width usec 0.88 1.6 HP-Filter MHz 4 1 LP-Filter MHz 20 10 Results We were successful in measuring the temperature dependents of the Young's and shear modulus, and Poisson ratio, but we not able to acquire the all bonding agents needed to do a complete sweep temperatures between 20 K and 300 K. We also were not able to control the rate of temperature change because the controller is broken. We were able to acquire data between the temperature range of 180 K and 300 K for the longitudinal wave velocity of Ti 3 Al C 2. This data will be reported along with the room temperature values for the Young's and shear modulus, Poisson ratio along with the calculated Debye temperature for these two carbides. The results can be found in figure 3. Table 3 Results Ti 3 Al C 2 a Ti 3 Al C 2 V 2 Al C Room Temperature (R.T.) longitudinal velocity m /'s 8880 9529 Not reported R.T. Shear Velocity m /'s 5440 5028 5764 R.T. Shear Modulus GPa 124 114 153 R.T. Youngs Modulus GPa 297.5 297.4 Not reported R.T. Poisson Ratio 0.220 0.307 Not reported Debye Temperature K 758 782 Not reported a.

These are the values reported from Dr. Peter Finkel [5, 7] Ti 3 Al C 2 Figure 4 shows the temperature depends of the elastic modulus for Ti 3 Al C 2. The temperature is ranging from 190 K up to 280 K. From 195 K to 233 K the elastic modulus increases approximately 12 MPa for every degree Kelvin. This does not include the spike found at 210 K. At 235 K the elastic modulus starts to decrees in value for every step in temperature. Between 255 K and 270 K there is a steady decrease of about 37 MPa per degree. There is a rapid drop at about 270 K. The slop is approximately 200 MPa per K. The elastic modulus seems to be at its stiffest point at about 235 K with a value of 411.54 MPa.

Fig. 8 the elastic modulus as a function of temperature for Ti 3 Al C 2 The room temperature longitudinal and shear velocities are 9529 and 5028 m / 's. The Youngs and shear modulus at room temperature are calculated to be 297.4 and 114 GPa, with a Poisson ration of 0.307. The Debye temperature is 782 K. This is in good agreement with the estimation calculated by Dr. Peter Finkel (he estimated a Debye temperature of 758 K) [7]. The longitudinal velocity 6.5% slower than the one calculated by Dr. Finkel, and the shear velocity was 10.4% faster [5, 7]. The Youngs modulus in the only result falls within the 0.03% of the value calculated by Dr. Finkel. V 2 Al C We were able to measure a reasonable shear velocity.

The measured shear velocity came out to be 5764 m / 's. The shear modulus is 153 GPa. This value is considerable higher than any I have seen for a layered ternary carbide, but is much lower than TiC 0.97 (the shears modulus is reported to be 207 GPa at room temperature) [8]. We will need a better sample to run to get more believable results.. Conclusion In this paper we presented a non-destructible method in investigating structural integrity.

The measurement of the transit times of the ultrasonic waves can be used to solve for the elastic and thermodynamic properties of the material. The results gathered by our measurements do not fit well with the results reported in ref. [5, 7]. This means that we must improve the current state of the set-up.

Bibliography

1.) Kenneth Warren, Big Steel, (Pittsburgh University Press, Pittsburgh, 2001).
2.) Bart Hopkins, Musical Instrument Design, (Sharp Press, Tucson, 1996).
3.) A. Wood, Acoustics, (Dover, New York, 1966).
4.) John Potter Shields, Basic Piezoelectricity, (Howard W. Sams, Indianapolis, 1966).
5.) P. Finkel, M.W. Barsoum, T. El-Raghy, Journal of Applied Physic, 85, 10 (1999).
6.) Ashley H. Carter, Classical and Statistical Thermodynamics, (Prentice Hall, Upper Saddle River, 2001).
7.) P. Finkel, M.W. Barsoum, T. El-Raghy, Journal of Applied Physic, 87, 4 (2000).
8.) M.W. Barsoum, Prog Solid St Chem, 28, pg 201-281, (2000).