Low-power electron paramagnetic resonance spin-echo spectroscopy

JOURNAL

OFMAGNETIC

RESONANCE

91,475-496

(1991)

Low-Power Electron Paramagnetic Resonance Spin-Echo Spectroscopy COLIN

MAILER,*

Department

o/‘Chemistry.

Ph1:Gc.y

University

DUNCAN

University (?fNm

A. HAAS, ERIC J. HUSTEDT, JAMES G. GLADDEN, AND BRUCE H. ROBINSON of Washington. Brunswick,

Seattle.

Fredericton,

Uhshingtton Nm,

Y81Y5;

Brunswick.

and

Canada

*Department

o/

E3B 5.43

Received May 15. 1990: revised August 3 I. 1990 Electron spin-echo experiments generally require microwave power levels of hundreds of watts to produce the 5-10 G of RF field to generate 90” and 180” pulses in 10 ns. A low-power (i.e.. less than 1 W) EPR spectrometer using a loop-gap resonator can generate the full range of time-domain experiments on samples with submicrosecond recovery times: 90” pulses are generated in 40 ns. and relaxation times as short as 22 ns are measured. Appropriate time-domain experiments were performed to independently measure the spinspin relaxation time, phase memory time. and spin-lattice relaxation time: the results were compared with CW saturation. It was found that the spin-spin and spin-lattice relaxation rates do differ by about 5%). The entire CW signal of PADS is reconstructed from a pulse experiment at a single field position. Small differences in linewidths among the three lines were seen in accordance with theory. cc IYYI Academic Press. Inc

EPR spectroscopy routinely involves a CW field sweep. The instrument for CW EPR is sensitive, convenient, and commercially available. The addition of pulsed technology to EPR provides the potential for advances similar to that seen in pulsed nuclear magnetic resonance ( 1): detecting the entire spin system at once, probing motional dynamics directly, controlling pulse sequences to perform multiple-quantum experiments (2)) etc. One of the major technical hindrances to the widespread application of pulsed EPR has been the need for hundreds of watts of microwave power to generate the necessary nanosecond pulses. Typical modern instruments ( 3, 4) use high-power RF sources (about one kilowatt) and low-c) resonator cavities for wide bandwidths (5). Such spectrometers can measure relaxation times as short as 50 ns. and can generate Fourier-transform EPR spectra that are 200 MHz wide. The development of low-Q resonators with both high filling factors and high-power density has changed the prospects for time-domain EPR (6). Hornak and Freed ( 7) demonstrated the feasibility of obtaining spin echoes from a solid sample with a loopgap resonator (LGR) at low microwave powers. This work now demonstrates that submicrosecond pulse experiments can be done on aqueous samples undergoing Brownian motion using conventional CW EPR instrumentation, involving only minor changes to the microwave bridge and the addition of high-speed data acquisition electronics. The ability to perform conventional CW EPR, ST EPR, and time-domain experiments with a single spectrometer makes for an extremely powerful combination. 415

0022-2364191

$3.00

(‘opynght 0 I99 I hy Academic Press. Inc All nghfs of reproductmn I” any form rerrrved

476

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INSTRUMENTATION

The block diagram of the apparatus, shown in Fig. 1, is a slightly modified version of earlier designs (8, 9). The instrument is structured after the standard three-arm system: the detector bias arm (top); a conventional CW EPR observe arm (middle), which takes one-tenth of the power from the klystron through directional coupler DC2; and an arm (bottom) for time-domain experiments, which is pulsed on and off by the high-speed microwave diode switch SW1 before directional coupler DC3. A mechanical microwave transfer switch allows one to choose to radiate the sample with either continuous power for conventional EPR or pulsed power for time-domain EPR. The bottom arm may be used for high-power CW (such as ST EPR) experiments. Both pulsed and continuous power may be applied to the sample at the same time by means of directional coupler DC3 for SR EPR experiments ( IO). The power incident on the cavity is measured by an HP 432A power meter with calibrated bolometer. The microwave signals from the sample pass from the resonator to the signal mixer

AUTOMATIC FREQUENCY I--------------‘-----------------------------------------------------------------. AFC

CORRECTION

CONTROL ERROR

SIGNAL

/

____----___________----------------------------------------------------

OBSERVE

ARM

POWER

METER

FIG. 1. Schematic of a conventional EPR bridge modified for time-domain spectroscopy. The extra components are the 10 dB directional couplers DC2 and DC3 (Hewlett-Packard HPX752C), waveguide attenuators ATT1 and ATT2 (Hewlett-Packard HPX382A). waveguide phase shifter PHl (Hewlett-Packard XSSSA), coaxial phase shifter PH2 (ARRA 9428A). isolators I2 and 14 (FXR X 157A). and the high-power microwave switch SW1 (Norsal Sl870D). This assembly is connected to the cavity via the waveguide transfer switch (FXR X64 I A). The power meter (Hewlett-Packard HP420B) is attached by a 20 dB directional coupler DC4. The components added in the signal detection channel are the limiter and low-noise 35 dB gain amplifier MPA (Systron-Donner SDA 9095-02). the blanking switch SW2 (Hyeltronics HSK13lB). and the isolator 13 (PRD 1203 ). The mixer was an RHG DMB- 12. Postmixer electronics include an antialiasing filter (K & L Microwaves 4Ll20-5L/B400-O/OP), wideband amplifiers (Xl0 Princeton Applied Research 115; X 10 and X5 Comlinear CLCIOO), and the transient recorder (Biomation 6500).

LOW-POWER

EPR

SPIN-ECHO

SPECTROSCOPY

477

through the transfer switch, a protect switch, a limiter, a 35 dB low-noise microwave amplifier, and an isolator. After down-conversion by the double-balanced mixer, the signal is filtered by a 250 MHz low-pass antialiasing filter, then amplified by 45 dB by wideband amplifiers and passed to the k-1 V input of a Biomation 6500 transient recorder. This transient recorder has a 6-bit digitizer with 2 ns sampling time and collects 1024 points for a minimum sample period of 2.05 /*s. The transient recorder is connected to a PDP- 11/23 computer via a custom-designed interface which can do high-speed signal averaging. The interface was constructed using standard NMOS RAMS and TTL family logic components and contains a 1024 word by 24 bit memory plus a high-speed adder. Each time the transient recorder completes a digitization of a 1024-point spectrum, the interface takes the digitized data from the transient recorder and adds (or subtracts) them to the existing contents of the interface memory. The operation proceeds at a rate of approximately 330 ns per point or about 338 ps for each 1024-point signal. The transfer of only 5 12 or 256 points from the Biomation can be done when faster signal averaging rates are needed. The microwave-pulse timing and the control of blanking, triggering, etc., are controlled by a custom-designed digital-pulse programmer, interfaced to the computer. The programmer was constructed using 10K series ECL logic components and can produce pulse sequences of up to 256 steps in length. The time duration of each step can be programmed to any period between 20 ns and 168 ms in 10 ns increments. The programmer controls 16 independent digital outputs, available as both ECL and TTL logic levels for maximum flexibility in connecting spectrometer components. A front panel switch register controls the quiescent state of the outputs, which can be useful for testing the spectrometer when the programmer is not running. Prior to the experiment, the timing and output-level-control information is transferred from the computer to the pulse programmer by loading the state of the output and its duration for each step into the pulse-programmer memory. The sample resonator is a Medical Advances Model EPR-XB 1 (Milwaukee. Wisconsin) loop-gap resonator. It has a loaded Q of 300 when it contains a 0.6 mm i.d. by 0.84 mm o.d. quartz capillary (Vitrodynamics, Rockaway, New Jersey) filled with an aqueous solution. The sample, 5 mm long, was an aqueous solution of 1.83 m M “N-peroxylamine disulfonate (PADS), saturated with 0. I M sodium carbonate and under a nitrogen atmosphere. BLOCH

THEORY

FOR

THE

EPR

SIGNAL

Consider a single spin-4 electron in the presence of a static magnetic field, H,,, along the z axis of the laboratory coordinate system. RF microwave irradiation, defined as 2hlcos(wt), is applied along the x direction. The components of the magnetization obey the Bloch equation of motion in the rotating frame ( 11): dM -=-A.M+Q. dt M contains the three components Q are defined as

of the magnetization.

The matrix A and the vector

478

MAILER

l/T2e

A=

[

A 0

ET

-A

0

1lT2e

reh

-y,h

l/T,,

AL.

1

and

Q=

[I4 fI

,

where q = xowo/ T1,. The counter-rotating components of the microwave field have been omitted. x0 is the magnetic susceptibility, and o. is the electron Larmor frequency. A = w - redo defines the resonance position, and 7e is the gyromagnetic ratio. CW

EPR

Under CW conditions, a modulation, continuous irradiation of the sample along the z direction, defined as h,cos( a,&), is added to the DC magnetic field Ho. The signal is obtained from a lock-in amplifier operating at w,, which is usually 100 kHz. The absorption signal, Mi, , is the y component of the magnetization in the rotating frame detected at the first harmonic with respect to the frequency modulation. Under conditions where the modulation amplitude is small relative to the linewidth, i.e., y,h, Tze < 1, we obtain ( I1 )

2A/ 7-2, ( A2 + 1 /SOT;,)( A2 + 1/S1 T;,) I ’ where 1

+

(-/eh,)2LT~e

(rT

-’

le%n)2

+

1

and Y = 0, 1,2, . . . is an index which refers to the harmonic of the modulation. When wm < l/Tie, S, - So = { 1 + (y,h, )2T2, T,, ) -’ and & is the saturation parameter as defined by Poole (12). Under this constraint, the equation for Ml. reduces to the familiar form of the first derivative of a Lorentzian:

2AlT2e M:,= qyehmh (A2 + 1/SoT$,)2

I ’

The values of A at which the peaks occur are Amax = f 1/ T2,a. L is the peak-topeak width of this line in gauss (L = 2 I Amax1/-ye), and it follows that

, where Lo is the peak-to-peak width in the limit of very low microwave power: Lo = 2 / fiT2e7e. Define AY’ as the peak-to-peak height of Mh. Substitution of the values of Amaxinto the equation for Mh gives AY’ = 1.3q-yeh,,,h,T&S:‘2.

131

At low powers, So is approximately unity and the signal is proportional to h, . As hl increases, So decreases and the signal levels off; at higher levels of h, , the term in to 1 /hi. So dominates and the signal decreases, eventually becomin1Jg yportional The peak-to-peak height will be maximized when h, = I / 27, T,,T2,; then SO = 3. The magnetization My is related to the out-of-phase component of the susceptibility,

LOW-POWER

EPR

SPIN-ECHO

SPECTROSCOPY

479

x”, by MY = h,x”. Similarly, the component of the magnetization generated by the field modulation at the first harmonic is related to the RF susceptibility: Mf.

= h,x”‘. Time-domain

EPR and Towey oscillations. When stimulated by magnetization precesses in the rotating frame around the effective (Torrey ) oscillations of the EPR signal (8, 13). Assuming that the onance ( LI = 0), one finds ’ from the matrix A that the eigenvalues are (13)

an RF pulse, the field to produce spins are on resor recovery rates

X2 = +{(T;,’

+- T;,‘) + i(T;,’

- T;,‘)’ - 4(y,h,)2}

Idal [4bl

x3 = ;{(Tr,’

+ T;,‘) - i(T?:

- T;,1)2 -4&h,)‘}.

[4cl

A, = { L-’

The relaxation rates of the dispersion and absorption FIDs are XI and X2, respectively. The third eigenvalue is the relaxation rate for the longitudinal magnetization and hence represents the rate of recovery of the true SR signal. When 2y,h, > ( TFJ - T;,’ 1 , Torrey oscillations will be produced, with a frequency given by

a: =z(r,h,)2

- (TG’;“:i’,

151

Whenever Torrey oscillations are observed, h, cannot affect the real parts of any of the three relaxation rates. If T$ = T;,’ , then the observer power produces oscillations with frequency UT = Y,h, (8). On the other hand, if T;d - T;J $ 2y,h,, then there are no oscillations and the apparent spin-lattice relaxation rate is given approximately as

which, for low observer power, reduces to X3 = T;k ( 14). The signal and magnetization. Abragam ( 15), in reviewing the work of Feher ( 16), describes the magnetic resonance signal, in terms of the RF susceptibility, x, as a voltage output from the detector or mixer, ?/, which is proportional to the incident voltage, V,,, which, in turn, is proportional to @; specifically, ‘V = V,,47rQx”. Mims (17) has given a relation between incident power in watts, PO, and the RF field h, in a resonator for unit volume of sample.

h: -zLy PO

2 =- 47~8 w

[61

where cyis the conversion factor between h, and power. By starting with the above relation, substituting for V, and taking the output signal to be proportional to V by a gain factor, g, we get Signal =

ga2X”&.

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This expression is the same as that given by Hyde (6). From the above expressions it follows that the signal can be written as Signal = g&2,x”, and the signal at the first harmonic of the modulation Signal’ =

gah,X"'

can be written similarly as

= golMj,.

171

This is perhaps a somewhat surprising result. The signal is proportional not only to the magnetization, as expected, but also to the conversion efficiency, a. These expressions are very useful for comparing characteristics of resonators when the signal gain, the modulation amplitude, and the sample size are kept constant. Under these conditions, the ratio of signal heights at the same h, in two different resonators-the LGR and the TEloz--should be (al( LGR)/ol( TE102)), and the ratio of the signals at the same incident power, PO, when the samples are well below saturation, should be ((Y(LGR)/cx(TE,~~))~. Froncisz and Hyde (6) defined the parameter A as the ratio of the RF magnetic field amplitudes in two resonators for the same incident microwave power, PO. Therefore

RESULTS

Loop-gap performance and h, calibration. The most direct, and reliable, way to calibrate the RF field amplitude is to observe the Torrey oscillations at various power levels (8). Unlike CW methods, this method is independent of any assumptions about T,, and Tze and does not require a field sweep calibration. Figure 2A shows Torrey oscillations obtained with the loop-gap resonator at 100 mW of incident power. After roughly I .7 PS,the FID is also collected. The Torrey-oscillation portion of Fig. 2A (data from 0.2 to 1.5 ys) was analyzed with linear prediction (4) (see Fig. 2B), which simultaneously determined the oscillation frequencies and the rates of decay. The fit consists of four oscillating components, which are listed in Table 1. The fourth component corresponds to the Torrey oscillations and the third to the oscillation of the center line. The origin of components 1 and 2 is unknown; they have rapid decay rates on the order of the cavity response time and may be associated with system artifacts. However, since these two components die away quickly, they do not perturb the analysis of hl . The Torrey oscillations may be understood using the above theory. which predicts that, for a line on resonance, oscillations may be induced when the field is sufficiently large, i.e., (27,/r,) > ( TFi - TTe]). From Eq. [ 51, the oscillation frequency for this case is given by u:: = (y,h,)2 - {(T;,’ Upon substitution

- T;,1)/2)*.

of the relation between incident power and field, one has a:. = (yea)‘Po - { (Ty: - T3/2}*.

[91

Therefore, a plot of ( wT )* versus power, as shown in Fig. 2C, should give a straight

LOW-POWER

EPR

SPIN-ECHO

481

SPECTROSCOPY

line with a slope of ( yea)’ and an intercept of { ( T,-,’ - T;d)/2 } 2. From the leastsquares fit to the data one finds that cy = 4.5 t 0.1 GW p”2, and, therefore, hi = 1.4 G when U,, = 100 mW. See Table 2. From the intercept one may estimate that (T3: - ‘r;,’ ) = 5 & 10 pss’ . The data of Fig. 2C are optimized to obtain a precise value for N, but, in view of the large error ofthe intercept, they are not useful for determining the relative values of the spin-lattice and spin-spin relaxation times. Under the same conditions that produce oscillations, the theory predicts that the rate of decay of the oscillating signal should be the average of the spin-spin and spinlattice relaxation rates, ( Tyi + ‘r;d )/2, which should be independent of the microwave power level. However. a weak correlation between relaxation rates and power level was observed, and it was measured to be around 6 ps~ ’ / W, with a 50%: error in this estimate based on data scatter. The extrapolation to zero pump power gave a rate of 3.0 iz 0.4 ps--’ The characteristics of different resonators may be estimated by various CW EPR techniques. Table 2 summarizes the results for the two different resonators: the LGR and TElol with a dewar insert. Figure 3A shows the effects of power on the CW linewidth. According to the above theory (Eq. [2]), a plot of the linewidth squared vs the incident power-f, vs PO-should give a straight line, with a slope of a*[ 47’,,j I 3 7‘2V/ ] and an intercept of Lij. The values for Lo were 0.255 + 0.0 17 G for the LGR and 0.32 I + 0.024 G for the TE,,,? cavity. The value of N for the LGR and the TE,,,2 cavity cannot be determined without a knowledge of T,, and Txe. However, the ratio of the cu’sfor the two different resonators is independent of any assumptions about the magnitudes of the relaxation times. In Fig. 3B the peak heights, AY ‘I, are plotted as a function of incident microwave power. According to the theory for a single homogeneous line (Eq. [ 31).

where the half-power point is f’,,? = [(Y~~)‘T,,T~~]~ ‘. aI”, is maximized when the incident power is 1 PI,?. The data are shown with the best least-squares fit based on the above equation. For the LGR, PI,: = 2.06 +- 0.06 mW and ga’ = 11.58 X lOi + ~- ?5 X lo’, and for the TE102 cavity, PII = 19.4 +- 0.52 mW and gn’ = 1.412 X IO’ f 2.5 X 1O3 in arbitrary units. From the fits to the two data curves, (Ymay be estimated. assuming T,, = T2, = 0.283 ps. Care was taken to ensure that signal amplification was the same for both the LGR and the TE ioZcavities, and the modulation frequency was set to IO kHz to remove frequency broadening in the EPR signal of PADS. The HD und the C’W EPR spectmm. Figure 4A shows the absorption and dispersion FIDs resulting from positioning the microwave frequency 4 G downfield from the center of the three-line PADS spectrum. One oscillating component of the two FIDs had an average period of 2 1.2 ns or 47.2 1 MHz. The observation of oscillations in the FID signal from a line which is off resonance by 13.06 G2 (18) suggests that the whole EPR spectrum can be stimulated in a single pulse and analyzed for the frequencies in the FID, as done in FT NMR (I) and in FT EPR (4). Table 3 lists the

’ The lines are - 13. I 18. 0.0, and 13.064

G at X band.

The total

is always

26.182

G

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(MICROSECONDS)

I.,,.I.,,.,

,..I_

0.5

1.0 TIME

I 1.5

QLS)

FIG. 2. (A) Torrey oscillations of magnetization produced by pump microwave field in the LGR. Conditions were 100 mW incident on the LGR for 1.5 ps. Blanking of 100 ns was applied at the onset of the microwave power and at the end of the I.5 PCSpulse to suppress transients. The residual magnetization at the end of the pulse appears as an FID at the end of the second blanking period. The EPR sample was a 1.83 mM 14N PADS solution in a 0.6 mm i.d. X 0.84 mm o.d. quartz capillary: 10 kHz Zeeman modulation frequency. 0.1 G peak-to-peak modulation amplitude, 0. I25 s time constant. ( B) Plot of the data in (A) (dotted line) with linear-prediction fit (dashed line) from 0.1 to 1.5 ps. See Table 1. (C) Plot of Torrey oscillation frequency squared versus microwave power. The slope of the line is yaol* and gives an N (power/RF field conversion factor) of 4.5 GW -“* for the LGR (see Table 2).

frequencies, amplitudes, and decay rates for the three lines for both the absorption and the dispersion components. Figure 4B is the EPR spectrum which results from using the data extracted from the FID with linear prediction followed by an analytical calculation of the Fourier transform, as a CW LP EPR spectrum (Za, 6). The linearprediction analysis of both the absorption and dispersion FIDs found a fourth relaxation

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SPIN-ECHO

483

SPECTROSCOPY

800,

0.00

0.02

0.04

0.06

0.08

0.10

Cl.12

Power(W) FlG.

2-Conhued

component labeled “extra” in Table 3. This component was not included in the reconstruction of the CW LP EPR spectrum. The FID with 90” and 180” pulses. When the value of h, is known, the time to produce a 90” RF pulse may be estimated from the relation -yehIT = 0, where the tilt angle is 13radians and the pulse time is 7. Figure 5A shows the FID obtained after a 424 mW pulse was applied for 40 ns. This pulse corresponds to a 90” pulse. The time needed to form the 90” pulse is about 10 ns longer than that theoretically estimated, and the difference is presumably caused by the finite response times of the microwave switch. The decay time ( Tze) of the FID is 288 ns, determined by a least-squares fit of the FID with a single exponential. Figure 5B shows the FID when the same pump power of 424 mW is applied for 80 ns. The absence of an FID from the on-resonance component indicates that there is little magnetization in the x-y plane, or that almost perfect inversion of the resonant spins and hence a 180” pulse have been achieved. The oscillating components in the signal seen in Fig. 5B correspond to the upfield lines which do not receive well-defined pulses. Figure 5C shows the effects on the FID of making the DC magnetic field inhomogeneous with the insertion of a shaped piece of metal (a screwdriver) into the magnet TABLE

I

Linear-PredictionAnalysisof the Torrey-OscillationData shown Component number I 2 3 4

rate (MHz)

Decay

50.8 28.2 4.86 3.78

Equivalent i-2,(ns) 20 35 206 264

Frequency (MHz) 60.3 20.0 36.75 4.07

in Fig. 28

Relative amplitude 17.00 3.38 0.086 1.oo

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ET AL.

TABLE 2 A Comparison of Resonator Characteristics Determined by Different Method

Resonator characteristics

Torrey oscillations

a( LGR) Q’E,od AZ A

4.5 f 0.1 -

CW EPR” line broadening 4. I5 I.5 7.6 2.76

+ k k f

0.06 0.08 0.8 0.15

CW EPR” saturation from PI,? 4.4 * 1.43 i9.4 + 3.07 f

0.1 0. I 0.4 0.07

CW EPR low power from gc:tu’

CW EPR signal rollover point

8.2 + 0.4 2.86 f 0.07

1.2 t 0.6 2.7 t 0. I

Now All error estimates are based on the errors from the least-squares fitting, propagated by Gauss’ formula, and are reported at a 95% confidence level (i.e., 2~): (Y is reported in units of Gauss/&% and .I - ~u(LGR)/(u(TE,~~). For the last three columns. refer to Eq. [IO]. a See Eq. [2]. b Errors in N are estimated assuming a 3% error in the relaxation times.

gap. The FID is obtained under the same conditions as those of Fig. 5A with the inclusion of DC inhomogeneity. Now the FID decay time is on the order of 22 ns, as compared to 290 ns for the FIDs shown in Fig. 5A. The CW EPR PADS spectrum peak-to-peak linewidth was broadened to about 3 G, corresponding to a Tz, of 25 ns. Spin echoes. The simplest spin-echo pulse sequence requires an initial r/2 pulse, followed by a mixing time, T, during which the spins dephase, and then a r pulse to reverse the precessional direction of the spins. The spins refocus and form the echo at time T later. For this experiment the microwave power was set to 424 mW, which produced a 40 ns 7r/2 and an 80 ns 7r pulse, as previously demonstrated in Figs. 5. The two-pulse sequence is usually modified to preserve the echo but suppress any FID from those parts of the sample which are not inverted by the T pulse. We used phase inversion of the a pulse (which leaves the sign of the echo unchanged but inverts the sign of the FID) and phase inversion of the a/2 pulse (which inverts the sign of the echo) (4). The two echoes shown in Fig. 6 have 7 delays of 300 and 400 ns, respectively. Calculating the rate of decay of the echo as a function of 7 is a means of measuring phase memory time TM, which, for a homogeneous line, should be equal to TZe and should be the intrinsic Tze regardless of field inhomogeneity. The observed echo heights will be in the ratio exp( -2 { (7, - T*)/ TM 1). The peak height of the 400 ns echo is 0.49 times the height of the 300 ns echo. The peaks of the two signals are separated by exactly 100 ns, as they should be. Analysis of the echo heights gives a value for TM of 280 ns (see Table 4). The shape of the refocused echo should ideally be the same as that of the FID (see Fig. 5C) ; however, in practice, it appears to be slightly broader and does not fit a single exponential. Saturation recovery. In the experiments which generate either an FID or an ESE there is no power incident on the sample during the observe period, whereas in saturation recovery there is. The system is initially pulsed to invert or partially saturate the magnetization. Figure 7A shows the FID, with the field centered on the low-field line, produced with a long (2 ps), nonselective, 100 mW pulse, followed by a 90 ns

LOW-POWER

EPR

0.000

SPIN-ECHO

0.020

485

SPECTROSCOPY

0.040

0.080

0.060

POWER

(WATTS)

B 4.2

-

3.6

-

3.4

-

3.2

-

3.0 -25

1

I

I

I

-15

-5

5

15

Power

25

(dBm)

FK;. 3. (A) Plot of peak-to-peak linewidth squared versus microwave power of the center line of PADS in the LGR and the TEIOZ cavity, with a least-squaresbest-lit straight line. The slope ofthe line is proportional to (7’. and the intercept is Li. See Table 2 for results. La values for the two lines are 0.255 +- 0.017 G and 0.32 I t 0.024 G. respectively. (B) a log-log plot of 1Y ‘, , the first derivative peak-to-peak signal height, as a function of the incident microwave power for the LGR and TE,o2 cavity, with the least-squares optimized tit to Eq. [2].

blanking period and an additional 50 ns initial period which is omitted from Figs. 7. Under saturation-recovery (SR) conditions, the longitudinal component of the magnetization, during the observing period, is coupled to the transverse components by a low-level, observing RF. The longitudinal component recovers toward thermal equi-

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I..l....l....l....l...

I....I....I....I

0.5

1.0 TIME

1.5

2.0

(ps)

B 60 50 a40 -

-

530 r

-

20 IO 01

A 100

300 FREQUENCY

FIG. 4. (A) Absorption (solid line) and dispersion (dashed 100 mW power pulse. The magnetic field was 4 G downfield sample to produce off-resonance frequencies for the three lines Table 3. The amplitudes, rates, frequencies, and phases were all ( B) Absorption spectrum calculated, as (noise-free) analytic the absorption FID as listed in Table 3.

500 (Mradkec)

700

line) FIDs of PADS, obtained after an 80 ns, from the center EPR line of the 14N PADS of approximately -26, 1 I, and 48 MHz. See determined from the linear-prediction fitting. functions, from the three exponentials from

librium with a time constant of T,,. 3 The leak-through of this component is superimposed on the FID as Fig. 7B demonstrates. The power level was -6 dB m or 0.25 mW during the observation, which converts to 0.07 12 G observer amplitude in the 3 The low-level

RF observer

may be considered

to be a low-power

readout

pulse.

LOW-POWER

EPR

SPIN-ECHO TABLE

Results

of Linear

Prediction

“N spectral line LOW

Middle High Fxtra

Decay rate (MHz) 3.556 4.164 3.614 44.00

Equivalent T,, ( ns)

spectral line Low Middle High Extra ’ The literature ” With respect

Decay rate (MHz) 3.838 3.674 3.781 19.20

260.5 272.2 264.5 52.1

of Fig. 4A

component Resonance frequency (MHz)

0.233 0.213 0.237 2.90

25.819 10.633 47.384 15.958

281.2 240.2 276.7 22.1

Equivalent Tze (ns)

of the FIDs

Derivative linewidth (G)

Dispersion

‘%

3

Analysis

Absorption

487

SPECTROSCOPY

Line separation (MHz)” -36.5 12 0.000 36.75 1 5.325

Relative amplitude 0.15 1.oo 0.10 43.61

component

Derivative linewidth (G)

Resonance frequency (MHz)

0.252 0.24 I 0.248 1.26

-~25.758 10.541 47.037 16.X27

values measured by CW EPR are -36.763 to the middle line in the table above

and 36.6 12 MHz

Line separation (MHz)” m-36.39 1 -0.092 36.404 6.194

Relative amplitudeh 0.16 0.87 0.10 0.93

(?4).

rotating frame. Even such a low power could drive a Torrey oscillation. The maximum frequency for such an oscillation would be 0.2 MHz or 1.25 mrad/s (which can be realized if the spin-spin and spin-lattice relaxation times are equal). Figure 7C shows the SR component of the signal with the FID removed. The SR signal was obtained by rerecording the FID + SR signal (as shown in Fig. 7B) but with the phase of the pump inverted by 180”. Phase inversion of the pump does not affect the sign of the SR component, but it does invert the sign of the FID component. Addition of the two spectra will cancel out the FID, leaving primarily the SR signal. ‘4s shown in Table 5, the amplitude of the FID component changes sign with the phase inversion. The accuracy of the phase inversion was tested on the pure FID (Fig. 7.4 ). When an inverted-pump-phase signal of Fig. 7A (spectrum not shown but data included in Table 5) was added to Fig. 7B. the signal was nearly completely canceled out. Each of the data sets in Figs. 7 includes a fit, as determined by linear prediction, superimposed on the data. The decay rates and frequencies (including those of the inverted-phase spectra) are given in Table 5. The data of Fig. 7A, the FID, show primarily two components: the first is nearly on resonance and the second is the upheld (or center) line. There is another component, found by linear prediction on this data set but not included in the table. corresponding to the high-field line that is roughly 72 MHz away and has a 3% relative intensity with respect to the low-held line. The inclusion of the SR signal then gives primarily the same two components with decay rates that are nearly the same. Note that the inclusion of the SR did not

488

MAILER

ET

AL.

contribute a third component. When the SR is analyzed by itself, as in Fig. 7C, the decay rate is still about the same as that found in Fig. 7B. This indicates that the rate of the SR component is nearly identical to the rate of the FID component (3.1 vs 3.3 /CC’). The SR signal is not just a pure exponential, as generally suggested by simple theory. Instead, the SR signal has a frequency of 0.203 MHz on top of the decay. Note that this compares very favorably with the 0.2 MHz Torrey oscillation, &mated above, as predicted for the case when the spin-spin and spin-lattice relaxation rates are nearly equal. DISCUSSION

Relative sensitivity qf LGR and cavity. This study extends the work of Hornak and Freed ( 7): A commercially available LGR, with an LYlarger than that previously used ( 7)) gives an improved signal-to-noise ratio for constant sample size and permits true ESE experiments with very modest power requirements. Table 2 summarizes the values of cycalculated. The various methods for measuring the relative performance of the LGR and TEio2 cavity, with dewar insert, give a value for A of a roughly threefold improvement in conversion efficiency. This is sufficient to make possible a wide variety of time-domain experiments with one watt klystron sources. For the LGR, (Ymay be found by direct measurement of Torrey oscillations. This method gave an LYconsistent with that obtained by CW methods, within experimental error. Relative performance, i.e., A2, may be estimated from the CW EPR methods without assumptions about the relaxation times. However, to obtain values of LY,the CW EPR methods do require a knowledge of the relaxation times. Inhomogeneous field broadening can be a source of error in the CW EPR measurements, but estimates of such broadening appear to be within the linewidth of the PADS samples. Two problems associated with obtaining reliable calibrations of hi by CW EPR techniques are inhomogeneous samples and high frequencies used in Zeeman modulation. For the PADS sample, the inhomogeneity is not great. Figure 3B demonstrates that the saturation characteristics of PADS are in excellent agreement with the theory for a homogeneous line. This point may also be demonstrated using the criterion of Zhidkov et al. (19), which shows that { Awe/ Awp} = q - 9, where Awe is the width of the inhomogeneous Gaussian broadening, Awp = 1/ Tl, is the true linewidth, and q is the ratio of the two microwave field amplitudes on either side of the rollover point at which the signal is half of its maximum height. On the basis of the least-squares fits to the lines, and the error in PI ,z (Eq. [ lo] ), one may estimate a value of q = 9.26

FIG. 5. FIDs of the low-field EPR line of PADS in the LGR obtained after a microwave pulse (specified for each figure) and 90 ns of blanking (or dead time). The FID was sampled for 2 PCS(at 2 ns/point for 1024 points). Signals were obtained in 10 s: 20,000 successive signals were averaged at a rate of 2000 per second. A further 10 s were spent approximately 50 G downfield, well off resonance, to obtain a baseline spectrum that was subtracted from the FID. (A) FID obtained after a 40 ns, 424 mW pulse (emulating a 90” pulse). (B) FID obtained after an 80 ns. 424 mW pulse (emulating a 180” pulse) The on-resonance magnetization has zero projection in the X-Y plane, indicating almost perfect inversion. The off-resonant lines do not receive a 180” pulse and hence some oscillatory magnetization does appear. (C) FID from the line, broadened to 3 G peak-to-peak line width ( j$, = 25 ns) by inserting a screwdriver into the DC magnetic field. Obtained after a 40 ns, 424 mW pulse (emulating a 90” pulse across the single line). The best-fit, single exponential (superimposed on the data) has a time constant of 22.0 ns.

LOW-POWECR

A

EPR

SPIN-ECHO

489

SPECTROSCOPY

200000

-100000 1 . 0.00

, 0.50

I . 1.00

.

.

I 1.50

.

I .2.00

TIME (MICROSECONDS)

6

20000

10000 i 5 z

0

-10000 0 00

0.50

1.00

1.50

2 00

TIME (MICROSECONDS)

0.0

TIME

(MkiOSECONDS)

2.0

490

MAILER

0

0.5 TIME

ET

AL

1.0 (ps)

1.5

2.0

FIG. 6. Spin-echo spectra of the low-field line of PADS using a (90”--i--180”---observe) pulse sequence for two 7 values of 300 and 400 ns. The pump times were 40 and 80 ns, with 424 mW of power. for the 90” and 180” pulses, respectively; 180” phase cycling of the 90” and 180” pulses was employed (see text). Echo envelopes were narrowed and residual FID effects were removed by magnetic field inhomogeneity. T:? - 50 ns.

? 0.4, which implies that the inhomogeneous broadening is less than half of the homogeneous linewidth. The full equation for the saturation of M, has been simplified here by assuming that S, = S,. This approximation is not valid when the modulation frequency is of the same order as T,,. In practice this means that, when using the typical Zeeman modulation frequency of 50 or 100 kHz, the analysis of the ower saturation curve will not give a true indication of the relaxation times if e TleTze > 1 ps, a value that is attained by spin labels moving with a correlation time slower than about 100 ns. We note also that care is required to position the sample exactly at the same place in the LGR each time. If this is not done the power-to-RF field conversion will vary. The active volume is only 5 mm long, and the sample should not be any longer than this to keep the water away from the electric fields surrounding the LGR. We have found that the optimum position is obtained when the resonant frequency of the LGR has been lowered, by positioning the capillary, to its minimum value. Because of the low Q of the LGR, obtaining absorption signals that do not contain dispersion components requires special care; this error was minimized by phasing the mixer detector such that the CW EPR lineshapes were symmetric. The data provide a rational basis on which to decide whether to use a LGR. When working near saturation, if A times more sample can be placed in the standard EPR cavity then the cavity will be better. If one works below saturation then A2 times more sample is needed before the cavity will be superior to the LGR. One common way to get more aqueous sample into a cavity is to use a flat cell in the TEro2 cavity, but then the N values are much lower, being 0.62 GW -I” for pure

LOW-POWER

EPR

SPIN-ECHO

TABLE Time-Domain

Torrey

Quantity

oscillations

7‘;; ( r;,’

Torrey-oscillation component of SR

measured

EPR

FID Two-pulse CW

ESE

Figure

and value

2C”

+ Tr,’ j = 3.5 + 0.5 (ps)-' 2

Ti,l ~ T;; < 0.323 f 0.008 (ps)-' (7-i;

+ 7-i;)

lPh

= 3.07 f 0.03 (/a)-'

LGR: 7-L = 257 k 18 ns TE1,r2: Tze = 204 k 15 ns

3A

T$ = 288 f 20 ns

5A

TM = 280 ns

6

T2,=274f19ns

4A’

FID

Tze = 297 k 1 ns

7A”

SR

T,, = 320 iz 20 ns

7Cd

FID

TT, = 22 ns

5C'

CW

LP EPR

of T,, and Tze

- Trh = 5 -c 10 t&r

2 CW

4

and CW Measurements

Technique

491

SPECTROSCOPY

EPR

T$ = 25 ns

Not

shown”

” See Eqs. [4c] and [5]. h From the average of the high-frequency component of the various linear-prediction tits, produced using different numbers of singular values. See Table 5. ’ Average value from the fits of both spectra in Fig. 4A. d Error represents only the variation among different linear-prediction tits of the same data set. ” TF, obtained under conditions of deliberate inhomogeneous line broadening

buffer and 0.96 GW-“’ for an 89% glycerol/buffer mixture (20). In order for the flat cell in a TEio2 cavity to equal the performance of the LGR, 7 times more sample near saturation and 50 times more sample below saturation are required. In practice the flat cell usually wins out by about a factor of four or so in the signal-to-noise ratio, requiring -200 instead of 1.S ~1 of sample. A reasonable compromise is the TEio2 cavity with the dewar insert, because an increase in sample size can more than compensate for the lower (Y, giving about a factor of two superiority in sensitivity over the LGR. Free-induction decay. The pulse time for a perfect FID should be very much shorter than any relaxation processes, and a 40 ns 90” pulse certainly satisfies this for the PADS samples considered here. The experiment shown in Fig. 5C was conducted on the PADS sample with an artificially shortened T2*, which corresponds to a linewidth of 3 G. The pulse of 424 mW for 40 ns covers the broadened line with an effective hi of 2.23 G and has sufficient

492

MAILER

ET

AL.

0

B

0

-50 PO

bx -100 < = -150 G-i

-200

0.5

1.0 TIME

1.5

2.0

(pus)

FIG. 7. (A) The FID from the low-field line at the end of a 2 /IS. nonselective, partially saturating 100 mW pulse, followed by a 0.09 ~LSblanking delay and no observer (first 0.05 ps of data omitted). The best fit as given by linear prediction (see Table 5) is superimposed on the signal. (B) The signal prepared under the same conditions as those for (A) with the addition of 0.1 mW of radiation during the observing period. The signal is composed of two components: the FID, as seen in (A), and the SR signal. The best fit, as given by linear prediction (see Table 5) is superimposed on the signal. (C) The spectrum of the SR signal only. This is the result of the addition of the spectrum shown in (B) to a spectrum acquired with a difference in pump phase of 180” (see under Results and Table 5). The best fit, as given by linear prediction, is superimposed on the signal.

LOW-POWEIR

EPR

SPIN-ECHO

TIME FIG.

493

SPECTROSCOPY

(ps)

I-Continwd

power to tilt all the spins in the single inhomogeneous line by 90” (21). An exponential “fit” to the FID yields a TT, satisfyingly close to that estimated from the CW EPR lineshape (see Table 4). The field homogeneity is deliberately distorted and the CW EPR lineshape is quite asymmetric. Note that decay times on the order of 20 ns are close to the response time of our spectrometer. The Q of the L,GR is approximately 300, which corresponds to an impulse response time of about 10 ns. Inspection of the early time period, with the microwave blanking switch open. shows a 10 to 90% rise time of about 15 to 20 ns. Although the Q ringing puts a fundamental limit on the rate of change of the magTABLE Linear-Prediction

Data

set

Data

Analysis

of Figs. 7A. 7B (Plus

Component number

Decay

rate

(MHz)

5 the Respective Equivalent time (ns)

Inverted-Phase Frequency (MHz)

Spectra).

and 7C Relative amplitude

1 2

2.53 3.37

395 297

0.31 I 36.33

I 2

2.34 3.45

428 290

0.310 36.33

-0.82 -0.17

FID + SR (Fig. 7B)

1 2

3.30 3.36

303 298

0.177 36.50

-2.10 -0.07

FID + SR” (Phase inverted)

1 2

2.88 3.21

347 311

0.220 36.52

-1.44 0.06

1

3.08

325

0.203

-3.33

FID (Fig. FID” (Phase

7A)

inverted)

’ Data

not shown.

(See figure

captions

for experimental

conditions.)

1.0 0.16

494

MAILER

ET

AL.

netization, the microwave limiter, the blanking switch itself, and the 125 MHz bandwidth amplifiers all have response times that are in the 5 to 10 ns range as well. We have made use of the off-resonance oscillations of the FID to calibrate the magnetic field scan ranges, which is particularly critical for the smaller scan ranges, where accurate measurements of CW EPR linewidths are important. The calibration is exact: The frequency of oscillations of the off-resonance lines seen in the FID, as shown in Figs. 4A, can be converted to a value in units of gauss off resonance, which can then be used to calibrate the scan range field controller. There is no need to make assumptions about splittings from standard samples. Time-domain generation qf CW EPR spectra. The oscillations visible in the FIDs shown in Fig. 4A (and also Figs. 7A and 7B) arise from the off-resonance EPR lines of the 14N PADS sample. Table 3 shows the line separations measured from the FID, in excellent agreement with reported values (22). Following Gorchester and Freed (4), the CW EPR spectra are generated using the results of the linear-prediction analysis of the FID signals. In this way CW EPR signals are obtained as though Fouriertransform techniques had been applied to the FIDs. The relative amplitudes of the CW LP EPR spectra are consistent with the falloff expected for the power levels applied. Standard magnetic resonance theory (21) predicts that a signal which is about 2.7y,hl away from the carrier will be down in amplitude by about a half. In the present case, this corresponds to 11 MHz for a 1.45 G RF field amplitude. For the large offsets present here, the theory predicts that the high- and low-field peaks should be about 10% of the center line, in agreement with the data of Table 3. The overall bandwidth response of the system is also limited by the Q of the resonator. Gorchester and Freed discussed the effects of Q, pulse duration, hi, and spectral bandwidth on FT EPR (4). The present system with a Q of 300 and a frequency of 9.3 GHz should have a half-power bandwidth of 3 1 MHz, showing that the spectrometer is primarily limited by the pulse power and not the Q of the LGR. These results suggest that FT EPR can be performed successfully on spectra that are 100 MHz wide with a modest increase in microwave power and a slight reduction of LGR Q. Indeed, as the linear-prediction analysis shows, the upfield line that is 73 G from the low-field line (which is on resonance) can be detected, at about 3% signal intensity, in the FID produced by a long nonselective pulse. Therefore, it is now possible, using time-domain EPR techniques, to obtain from slowly tumbling nitroxides CW EPR signals with comparable signal to noise (4). The FT EPR data are capable of giving not only very high-resolution field splittings but also very precise linewidths. The Tze values given in Table 3 have approximately the same rate, but the center line has a shorter Tze than the others, corresponding to a 38 mG greater linewidth. Second-order hyperfine theory predicts that the center line should be split into two lines separated by a frequency of approximately (Ag/vo), where A0 is the hyperfine splitting in megahertz and vo is the microwave frequency, also in megahertz (23). This separation is about 130 kHz, or 46 mG, and agrees well with the experimentally found extra broadening of 38 mG. Such small differences in linewidth would be hard to measure by CW EPR spectroscopy. Measuring T,, and TJr. The T,, and TZefor a sample of PADS thoroughly nitrogen saturated (or degassed) were -320 _t 20 ns. Care must be taken, for oxygen dissolved in the sample can shorten the relaxation times to about -300 ns. We have shown

LOW-POWER

EPR

SPIN-ECHO

495

SPECTROSCOPY

that the relaxation times (summarized in Table 4) measured by the various timedomain techniques, including FID, SR, ESE, and Torrey oscillations, are consistent with the CW methods of line broadening and power saturation, as shown in Fig. 3 and Table 4. The SR spectra of Figs. 7B and 7C confirm that the FID can be suppressed by pump-phase cycling, and that T,, can be measured directly from the SR signal. It is important to note that the FID can be larger than the saturation-recovery signal. This is reasonable because the SR signal is the x component of the (slightly) tilted z magnetization and is proportional to observer amplitude, while the 90” pulse FID is the total magnetization. Increasing the observer power in an attempt to increase the SR signal runs into the problems of the observer power either producing Torrey oscillations when T,, - Tie or shortening the apparent T,, when T1, > T,, as described above. In the particular case of PADS, since the Torrey oscillations can be induced at low observer levels, care must be taken either experimentally or in the data analysis to consider such effects. CONCLUSIONS

A conventional CW EPR spectrometer can be modified to produce spin echoes from an aqueous sample, using a commercially available LGR, with a relatively large conversion efficiency, CY.The spectrometer can continue to be used for linear EPR and ST EPR. The modifications provide one with the additional flexibility for performing the FID, ESE, and SR time-domain experiments. With this type of modified spectrometer, it is convenient and routine to calibrate to a high precision both the field scan range and the microwave amplitude in the rotating frame. T,, and TZr from PADS samples have been directly measured by SR and FID, respectively. These values have been confirmed by ESE, and the difference between T,, and Tz, has been measured by SR. T1, - Txe for PADS, and they differ by about 5%. The LGR now makes it possible to cover a 200 MHz spectral range with a nonselective pulse for the FID data and to obtain a 40 ns 90” pulse with a modest (- 1 W) microwave power level for ESE. ACKNOWLEDGMENTS We acknowledge the supportof the National Science Foundation (NSF 87-20099), the National Institutes of Health (GM-32618) and the Natural Council (NSERC) of Canada. as well as the Exxon Education Foundation

Grants DMB-87-06 I75 and DIRScience and Engineering Research and IBM.

REFERENCES 1. T. C. FARRAR

Methods,” 2.

(a)

AND E. D. BECKER,

Academic

E. J. HUSTEDT,

Press, New H. THOMAN.U,

“Pulse York. AND

and Fourier I97 1.

Transform

B. H. ROBINSON,

NMR:

J. Chem.

Introduction Phr>,r

to Theory

92, 978 ( 1990):

and (h)

H.

THOMANN, H. Y. JIN, AND G. BAKER, Phjs. Rw Mt. 59, 509 ( 1987). 3. R. W. QUINE, G. R. EATON, AND S. S. EATON, Rev. Sci. In.strlcm. 58, 1709 (1987). 4. J. GORCHESTER AND J. H. FREED, J. (‘hem. Phw 88, 4678 (1988).

5

“Pulsed EPR Spectrometers,” troscopy. J. H. Peisach,

6. W. FRONCISZ 7. J. P. HORNAK

Compiled by NIH Biotechnology Resource Director. December 1986. AND J. S. HYDE, J. ,Map. Rcwn. 47, 515 ( 1982). AND J. H. FREED, S. Mqp~ Resnn 62, 3 I I ( 1985).

Center

in Pulsed

EPR Spec-

496 8. Y. 10. II. 12. 13. 14. IS. 16. 17. 18. 19.

MAILER

ET

AL.

M. C. T. B. C.

HUISJEN AND J. S. HYDE, Rev. Sci. Instrum. 45, 669 ( 1974). MAILER, J. D. DANIELSON, AND B. H. ROBINSON, Rev. Sci. Instrum. 56, 1917 ( 1985). SUGANO, C. MAILER, AND B. H. ROBINSON, J. Chem. Phps. 87,247s (1987). H. ROBINSON, J. Chem. Phys. 78, 2268 ( 1983). P. POOLE, “Electron Spin Resonance: A Comprehensive Treatise on Experimental Techniques,” 2nd ed., Wiley, New York, 1972. The S,, parameter is defined on p. 590. P. W. PERCIVAL AND J. S. HYDE, Rev. Sci. Instrttm. 46, 669 ( 1975). J. S. HYDE, in “Time Domain Electron Spin Resonance” (L. Kevan and R. N. Schwartz, Ed%). p. 13. Wiley, New York, 1979. A. ABRAGAM, “The Principles of Nuclear Magnetism,” pp. 75-76, Oxford Univ. Press, London, 196 I G. FEHER, Bell S.wt. Tech. J. 36, 449 (1957). W. B. MIMS, in “Magnetic Resonance in Liquids” (S. Geschwind, Ed.), Chap. 4. Plenum Press, New York, 1972. R. J. FABER AND G. K. FRAENKEL, in “Biological Applications of Electron Spin Resonance” (H. M. Swartz, J. R. Bolton, and D. E. Borg. Eds.). quoted on p. 100, Wiley. New York, 1972. 0. P. ZHIDKOV, V. I. MUROMTSEV, I. G. AKHVLEDIANI, S. N. SAFRONOV, AND V. V. KOPYLOV, Sav. Phys. Solid Slufe 9, 1095 (1976). The r.h.s. of the equation should be (q - 9.26) rather than

(4 - 9). 20. A. H. BETH, J. H. PARK,

K. BALASUBRAMANIAN,

J. Phy.s. Chem.

87,359

B. H. ROBINSON,

L. R. DALTON,

S. D. VENKATAMARU.

AND

( 1983).

“Principles of Nuclear Magnetic Resonance in One G. BODENHALJSEN, AND A. WOKUN. and Two Dimensions,” pp. 119- 122, Clarendon Press. Oxford, 1987. 22. H. M. SWARTZ, J. R. BOLTON, AND D. C. BORG, “Biological Applications of Electron Spin Resonance,” p. 100, Wiley-Interscience, New York, 1972. 23. J. E. WERTZ AND J. R. BOLTON, “Electron Spin Resonance: Elementary Theory and Practical Applications,” p, 449. McGraw-Hill. New York. 1972.

21.

R. R. ERNST,