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q = 2n/A (2)
For



Л

(3)
в < 1, the grating constant
can be determined by the equation


лh
2nin(@ /у)

Figure 1. Schematic of the laser-induced thermal grating technique.
Л =
Probing laser Signal and data processing
Excitation of thermal grating Detection of signal
Л is typl.cally about 50 /~m, which corresponds to an intersection angle of about 0.55°
Because of the volume thermal expansion of the sample the thermal grating causes a grating-like modulation sample, of refractive index An(t) = (dn/dT) AT ( t ), which acts as an optical phase grating and can thus be detected with a probing laser beam of wavelength ) X_p = 632.8 nm. Accordding to diffraction theory [6-8], the intensity of the first-order diffracted beam, I_±( t ), is proportional to the square of the maximum phase variation of the grating, Ф_т(t), which is written as

ф_т(₍) = гя^ = ^)АГ ( t) ) (4)
2ndAn(t) 2nd (dn
Therefore, the time dependence of the diffracted intensity I_t( t ) after the heating
pulse is I_± ( t )ae^-2t/T (5)
The thermal diffusivity a is then deter-mined as
^a = Vrq2 ⁽⁶⁾
In the present measurement, the modulus q of the grating vector is determined by measuring the diffraction angle 0s instead of the intersection angle of the two heating beams, в [9]:
q = T ^sin°_s (7)
Due to optical imperfections (e.g., Gaussian intensity distribution of heating beams and focusing), the diffracted light signal has a narrow distribution centered at q = (2n/X_p)sin 6_S [7]. In order to determine the diffraction angle 0s accurately, a measuring setup was developed (Fig. 2), with which the intensity distributions of diffracted beams of+1 and - 1 order can be measured with the photomultiplier tube. The distance between the two peaks of the intensity distributions AX is then determined by a computer (Fig. 3). Therefore, we can calculate the diffrac-tion angle 6_S from the geometrical relationship, and the modulus q of the grating vector can be determined using Eq. (7). The accuracy of the determination of 6_S and q in this manner is estimated to be better than + 0.55% [9].
In order to determine the relaxation time T, the first-order diffracted intensity I_t( t) is detected in the homo-dyne scheme by the photomultiplier tube exactly at the measured diffraction angle 6_S. The output signal u(t) from the photomultiplier tube is
then amplified and recorded by the transient recorder. The acquired data are fitted to the following equation with the least-squares method to obtain the relaxation timer:
I_± ( t ) av( t ) = Ae~^2t/T + C (8)
which can be measured with a photomultiplier tube (PMT) and a transient recorder. As a result, the time constant —/2 can be evaluated with which the intensity I_t( t ) decays exponentially.



Figure 2. Measurement of scattering angle 6_S.


Figure 3. Measured diffracted intensity distributions of+1 and - 1 order to determine
Heating beams Diffracted beams PMT Amplifier
the diffraction angle 6_S.
,[(2ir/A_p)sin 0_s] ^


Figure 4.Typical diffracted signal [output voltage v(t) from the PMT] for a mixture of water with 60% methanol (weight fraction w i=60%) at 295.53 K. The circled dots represent experimental data; the line is the exponential least-squares fit to Eq. (8) with relaxation time t.


Figure 5. Schematic of the test cell. 1, Cylinder of stainless steel; 2, glass window; 3, liquid volume; 4, mounting ring; 5, connecting piece; 6, O-ring of EPDM 211-70; 7,
8, bores for Pt-100 resistance thermometers.

RESULTS AND DISCUSSION

Using the laser-induced thermal grating technique, the thermal diffusivity of aqueous solutions of methanol has been measured at atmospheric pressure and in an extended range of temperature, 295-335 K. The measurement results are listed in Table 1.
Table1. Results for Thermal Diffusivity of Aqueous Solutions of Methanol as a Function of Temperature and Weight Percent Methanol at Atmospheric Pressure

Weight Percent Methanol
	20%		40%		60%		80%
T