Special Invited Review Scanning transmission electron microscopy*

Transcription

1 (0 Journal of Microscopy, Vol. 100, Pt 3, April 1974, pp Received 22 October 1973 Special Invited Review Scanning transmission electron microscopy* by ALBERT V. C R E w E, Departments of Physics and Biophysics and Enrico Fermi Institute, The University of Chicago, Chicago, Illinois SUMMARY The scanning transmission electron microscope is of quite recent origin, and it is only in the last few years that it has been shown that this instrument is capable of giving the same high resolution as the conventional electron microscope. In this article we examine the conditions necessary for the achievement of high resolution and also the various modes of contrast which can be obtained from this instrument. Finally, we suggest other ways in which the microscope can be used in future investigations. The electron microscope of conventional design (CEM) has long held the preeminent position in high resolution studies of very small objects, particularly objects which cannot be crystallized. In these pages it is hardly necessary to point out the achievements and limitations of this instrument. At voltages of about 100 kv a resolution of nm is possible, a value which is determined by the basic properties of magnetic lenses and the wave nature of the electron. Although occasionally used in dark field, it is more often operated in bright field. At high resolution one must use very thin specimens in order to avoid multiple scattering with its consequent image degradation and then the specimen is best treated as a phase object. Good phase contrast can best be obtained by a small amount of defocusing. A compromise must therefore be effected between the contrast and the modulation transfer function of the microscope. A great deal of the current work of microscopists is concerned with the understanding of this compromise (Heidenreich, 1964). More recently another instrument has been developed which is competitive in performance, the scanning transmission electron microscope (STEM) (Crewe & Wall, 1970). It is sufficiently different in construction, operation and capability to warrant separate consideration, and this is the purpose of this article. The STEM operates by scanning a finely focused beam of electrons across the specimen. Transmitted electrons can be detected and the resulting electrical signal used to modulate the brightness of a synchronously scanned display tube. It is only very recently that the resolution of such a device has been shown to be virtually the same as that of the CEM (Zeitler & Thomson, 1970; Wall et al., 1973a). So far it has been operated mainly in-focus with dark-field contrast, * Work supported by the U.S. Atomic Energy Commission. 247

2 Albert V. Crewe although recent calculations indicate that efhcient phase contrast can also be obtained (Rose, 1973a). Most of the developmental effort on this type of machine has taken place in our own laboratory, and the majority of this work has been on the technological aspects of the instrument (Crewe, 1970a). Applications have been few so far, and we can assume that the full potentials and capabilities of the STEM will not be known until it comes into more general use. ELECTRON OPTIC DESIGN We imagine electrons to be emitted from a perfect point source and being imaged by a lens. Then for a small aperture in the lens the image would be an Airy disc produced by diffraction at this aperture. As the aperture is increased the effect of diffraction decreases, but the effect of the spherical aberration of the lens increases. The optimum condition, that is, the one producing the smallest image, is such that the half-angle of convergence a0 is given by (Haine & Mulvey, 1954): where X is the wavelength of the electrons, and C, is the coefficient of spherical aberration. With this aperture the radius of the spot to the first zero is given by ro = 0.43C,1 4X3 4. The intensity distribution is then very similar to that of an Airy disc, although the intensity in the central spot is now 69 %, of the total instead of 81(y0 for the Airy disc. The quantity ro therefore defines the instrumental resolution if one uses a modified Rayleigh criterion, namely, that two points are resolved when the peak of one spot is located at the first minimum of a neighbouring one. It is therefore the optimum resolution of a scanning microscope providing the image of the source is sufficiently small. It is also the optimum resolution of a conventional microscope because we can simply reverse all the rays and consider the electrons to emerge from a perfect point source in the specimen plane. This value of the optimum resolution will only pertain when the electrons emitted by such a point source illuminate the aperture uniformly. For most cases, then, the ultimate resolution of the two types of microscope should be the same. For the STEM we must make the Gaussian image of the source small (in the nm range) and therefore demagnification must be used, and this reduces the intensity available in the probe. The problem of attaining high resolution is therefore intimately related to that of attaining adequate intensity. We therefore turn to the question of electron sources. The quantity of interest here is the brightness of the source. The concept of brightness in electron beams is much discussed but ill-used, so we will treat the matter with some care. If an electron source of area A emits a current of electrons I into a solid angle R at a voltage V1 we define the brightness as B=- I AR and we define the specific brightness as PI-. I AR V1 248

3 Scanning transmission electron microscopy In these definitions we emphasize that the source area A is a real quantity which does not depend upon any aberrations that might exist in the source region. Specifically A is independent of SZ. When is small (1 sr or less) and the source is a disc of radius A we can write where a is the half-angle of emission. Now let us suppose that these electrons are accelerated to a new voltage V by an aberration-free system. Such a system will, in general, have a first order magnification (M) so that the image (real or virtual) will have a radius M and the new value of the semi-angle will be (cc/m)z/v1/v. The factor dvl/v enters because the transverse momentum is conserved in the acceleration process. Therefore the brightness B is increased by a factor of V/V1 but the specific brightness is unchanged, because the specific brightness is defined as B divided by the voltage at which B is measured. It is for this reason that specific brightness is a more useful concept. In the case of magnetic focusing in the absence of electrostatic fields the quantity aa is conserved at successive images (Liouville's theorem) so that if the total emitted current is imaged we have I = Pn2a2A2V where V is the voltage through which the beam has been accelerated at the image. We now consider a real system and include a consideration of aberrations. We only need to know the net aberration coefficients (C, for spherical and C, for chromatic aberration) and the total magnification M of the entire system. Due to the aberrations we can only obtain a small probe size by limiting the value of 01 at the probe to some new value 01, and therefore the probe current is now I, = /3n2uO2A2M2V. We choose to write AM = cr, where r, is the theoretical probe size determined by diffraction and the aberrations, that is, the probe size resulting from a point source. If our actual probe size is to approach the theoretical value we must have E << 1. We now can write I, = /3n2ao2r,2 2V. But we have seen that in the case of spherical aberration effects the probe radius is the same as that produced by diffraction alone. (The same is true for chromatic aberration.) Therefore we can write u0~, = 0.61h where h = 1.25/.\/ V in nm. The probe current (in electrons/second) is then I, = 57400/3~~ (P in el sec-l nm-' sr-l V-l). This equation gives a very simple way to calculate the probe current in any scanning microscope. It should be noted that the operating voltage of the microscope does not appear in the equation. 249

4 Albert V. Crewe We need only add that the final probe radius can be written in terms of E. If the diffraction limited resolution is 6, we can include the effect of source size as 6 = 46,' + A2M2 because the two contributions are independent. Therefore 6 = 6,2/ The specific brightness p therefore determines the value of E achieve for any selected value of Zo. which we can CHOICE OF ELECTRON SOURCE There are several types of electron source having different values of B. We must choose the most appropriate one for use in the microscope. First we consider thermal emission from a tungsten filament. Haine (1961) gives a value for B of lo3 A nm-2 sr-l at 50 kv. This gives p = 1.2 x lo5 el sec-i nm-2 sr-l V-' and therefore I, = 6.88 x lo5 el/sec = x A. Next we take the lanthanum hexaboride source developed by Broers (1973). He quotes the brightness at 5 x lo5 A nm-2 sr-l at 75 kev, giving Zo = 2.3 x lo8 2 el/sec = x A. Finally we take the field emission source (Crewe et al., 1968). Such sources can readily emit a total current of 10 pa at 3 kv. Estimates of the cone into which these electrons are emitted vary, perhaps because the precise optics of the electron trajectories depends upon the shape of the tip and its support. However, from our own observations, a pessimistic value for the semi-angle of the cone would be 30". The effective source radius can be estimated at 1 nm, a figure which seems to agree with observations. This gives a specific brightness of 8.1 x lo9 el/sec-' nm-2 sr - V and we have Zo = 4.72 x 1O1O el/sec = 7.8~~ x A. We now examine what incident current we need in order to produce a micrograph. A good quality image might be considered to contain 1000 x 1000 picture elements and have lo4 incident electrons per element. If such a picture can be obtained in 10 sec, focusing and photography would not be too tedious. With this assumption, we have I, = lo9 el/sec N 1.6 x IO-lOA. At the other end of the scale we might consider a 500 x 500 element picture containing lo3 electrons per picture element where the picture is obtained in 100 sec. Under such conditions focusing is difficult, and the picture quality would be barely tolerable. We then have 250 I. = 2.5 x lo6 el/sec = 4 x 10-13~. We can now readily calculate the values of E which can be obtained for the

5 Scanning transmission electron microscopy three types of electron source. This is shown in Table 1. The calculations indicate that only a field emission source can produce a high quality micrograph at a resolution close to the optimum. A LaB, source can produce a poor quality micrograph at this resolution, but a tungsten filament would be undesirable. As confirmation of these calculations on field emission sources, we will use the example of one of our existing microscopes. This has an optimum resolution of 0.25 nm and operates with M = 1/33. This gives E = 0.12, and we calculate I, = 1.1 x A. The measured value of I. is A. This agreement may be fortuitous, however, since there is a considerable variation from tip to tip. Experimentally we observe variations of about a factor of two in both directions. Table 1. Micrograph Tungsten Field quality filament LaB, emission Good = 37 E = 2.05 E = 0.14 sjs, = 37 8/80 = 2.28 SjS, = 1.01 Poor = 0.10 E = E = 1.87 sjs, = 2.11 s/so = S/6, = THE INSTRUMENT We will not enter into the details of instrument design because this topic has been extensively reported in the literature (Crewe & Wall, 1970; Crewe, 1970a, b). However, the principles are clear, and from the preceding section we can readily determine the parameters of a high performance scanning microscope. We first of all select a field emission source for the reasons given. Such a source operates at a few kv so that we need additional acceleration to produce a beam of electrons in the range kv. The simplest electron gun is therefore in the form of a triode assembly. The aberrations introduced by such a gun should be small; preferably small enough that in the final probe these aberrations can be neglected compared to those introduced by the probe-forming lens. We chose the shaped anodes shown in Figs. 1 and 2 because calculations indicate that the aberrations are low. In addition, the electric fields everywhere are calculable, and both first and third order focusing properties can be determined (Crewe et al., 1968; Butler, 1966; Crewe, 1973). The electron beam emerging from the gun can be focused directly by a probeforming lens (Crewe & Wall, 1970). A microscope which we have built using this principle is shown schematically in Fig. 1. This system, however, has the disadvantage of inflexibility. The demagnification of the entire system depends upon the operating voltage of the microscope because the first order focal properties of the gun change with voltage. Therefore because we are interested in a small range of M (because the probe current is proportional to 1/M2) the range of operating voltages of the microscope is small. Nevertheless, we have been able to show that high quality micrographs can be obtained with a resolution of about 0.25 nm at an accelerating voltage of 40 kv (Wall et al., 1973a). One can overcome the inflexibility of this system by introducing a condenser lens between the gun and the probe-forming lens. In this case the instrument can be operated over a wide voltage range since the total demagnification can be controlled by that lens. A microscope which we are now operating uses this system (Crewe & Retsky, 1972) and is shown in Fig. 2. While this instrument was 25 1

6 Albert V. Crewe Field emission source --- / Gun -- Deflection coil-01 - K [ 'F Deflection coil- Lens field - -~ D :flection CMI- DE Ann ular detector -c L _I Spectrometer detector i Knife edge Spectrameter I- n Unscattered electrons Elastically scattered a Inelastically scottered Fig. 1. Schematic diagram of a scanning electron microscope using only one lens. Deflection coils above the lens produce the scanning raster on the specimen. The deflection coils below the lens restore the electron beam to the optic axis. An arrangement of detectors is shown which will give signals proportional to the elastic scattering (annular detector) and inelastic scattering (spectrometer detector). The focal length of the lens is 1.15 mm and the spherical aberration coefficient is 0.4 mm. The resolution of the microscope is approximately 0.25 nm. designed for 100 kv it is currently being operated at 50 kv where we have obtained a resolution of nm. CONTRAST AND DETECTOR DESIGN There are a number of different possible interactions between a beam of electrons and a thin object such as a microscope specimen. Therefore for a monoenergetic incident beam of definite angular extent the emergent beam is not mono-energetic and the distribution of electrons with angle is changed. The art of achieving contrast is that of deploying electron detectors in such a way as to take advantage of these changes. The characteristics of electron scattering depends on thickness, density and atomic number (Z). These parameters will vary with position in the specimen, and therefore suitable detectors can provide contrast. As a matter of general principle, the only quantities which can be determined and measured are the angle of scattering and the energy of the emergent electrons and their phase relationship with the incident beam. While it might be possible to arrange a system of detectors to obtain all this information, it is worth examin- 252

7 Scanning transmission electron microscopy Field emission tip-100 kv Gun < Condenser lens Double deflection ond stigmator Defining aperture Objective lens Double deflection Elastic electrons Fig. 2. Scanning electron microscope using two magnetic lenses. The condenser lens is used to produce a parallel electron beam for insertion into the objective lens. The detector arrangement consists of an annular detector for the elastically scattered electrons and one other detector which produces a signal which is the sum of the unscattered electrons and the inelastically scattered electrons. Focal length of the objective lens is 1.1 mm. The spherical aberration coefficient is 055 mm. So far the microscope has operated at 50 kv with a resolution of 0.3 nm or better. ing the anticipated results carefully in order to see if is it possible to simplify the detector design. ELASTIC SCATTERING We first examine the elastic scattering process. In this process the incoming electrons can be scattered by the screened Coulomb potential of the individual atoms in the specimen. Several such potentials have been proposed, of varying degrees of accuracy. For our present purpose it is sufficient to take the Wentzel potential which utilizes a simple exponential screening When this potential is used Lentz (1954) has shown that the total scattering cross-section can be written as z4/3 u, = (nm' per atom) V and the angular distribution has the form 1 253

8 Albert V. Crewe where 8, is given by Xz1i3 8, = - 2nao and a, is the radius of the hydrogen atom. The expected angular distribution is then constant at small angles and decreases as O4 at large angles. One half of all elastic scattering events occur at angles greater than 0,. It is clear that the relationship between a, and 8, is important and we can readily use the equations already given to show that - 58,Z1 3 (8, in nm). 254 Fig. 3. The micrograph showing single uranium atoms (the bright spots) on a thin carbon film. Full scale dimension is 29 nm. Note that three uranium atoms in the lower right hand corner are just resolved. (Photo by M. Retsky.)

9 Scanning transmission electron microscopy Therefore, for any existing microscope system 8, > 01, and consequently most of the elastically scattered electrons occur outside the cone of unscattered electrons. This means that a detector in the shape of an annulus can be used. The annulus should be such that the inner radius corresponds to 01, (or slightly greater) and the outer radius should be several times 8,. The use of this type of detector has already been shown to be extremely effective and is the equivalent of dark-field microscopy (Crewe, Langmore & Wall, 1970). The collecting power of such a detector has been analysed theoretically using more accurate atomic potentials and is about 80% efficient at 0.3 nm resolution (Isaacson, Langmore & Wall, 1974). Figures 3 and 4 are micrographs obtained with the microscope shown in Fig. 2. They were obtained using an annular detector and show single atoms of uranium (Fig. 3) and silver (Fig. 4). The specimens were prepared by placing a droplet of a dilute salt solution on a thin carbon film. Fig. 4. Micrograph showing single silver atoms (the bright spots) on a thin carbon film. Full scale is 29 nm. This micrograph appears to be of poorer quality than the uranium atoms in Fig. 3. The reason for this is that the elastic scattering cross-section of silver is approximately three times less than for uranium. This is probably close to the threshold limit of detectability under these conditions. (Photo by M. Retsky.) 255

10 Albert V. Crewe INELASTIC SCATTERING Energy can be transferred from an incident electron to the atoms and molecules of the specimen in a variety of ways. It is not our purpose here to enter into any detailed analysis of these mechanisms, and we will only summarize the situation in the broadest generalities. In the region of 0-50 V energy loss the spectrum of such losses for most substances shows a roughly symmetrical peak at V, and most of the energy loss events occur in this interval (Isaacson, 1972). The angle of scattering can be estimated using conservation of energy and momentum to be N A V/2 V where A V is the energy loss. Taking A V = 20 V we see that these angles are all much smaller than a0 for any microscope with I.'in its usual range (say > 10 kv). Therefore the energy loss electrons are substantially contained within the cone of unscattered electrons. The total inelastic scattering cross-section can be related to the total elastic scattering cross section by the approximate relationship (Crewe, 1970a) Z U,/Ui = If we wish to use the inelastic events to provide contrast they must therefore be separated from the no-loss events within the same cone. Therefore some kind of energy separation must be performed and a spectrometer is perhaps the most convenient and reliable method. Using a spectrometer we can obtain two signals, one corresponding to the no-loss electrons and one corresponding to the energyloss electrons. In using energy-loss electrons to provide contrast it should be noted that in general they will not permit obtaining as high a resolution as elastically scattered electrons. Inelastic events are non-local in character, a fact which can be seen from the fact that the scattering angles are so small. Rose (1973b) has investigated this point and concluded that the resolution using inelastically scattered electrons is limited to 1 nm. Although far from the limit available with elastic scattering, it is adequate for many if not most investigations. We can therefore conclude that a simple disposition of detectors consists of an annular detector followed by a spectrometer. Such a system can provide dark-field elastic contrast (annular detector), inelastic dark-field contrast (energy-loss detector) and bright-field contrast (no-loss detector). The dark-field contrast can be as much as 80% efficient and allow the highest resolution of which the microscope is capable. The resolution of the inelastic dark-field mode will be restricted to 1 nm because of the non-local nature of the scattering process, but will not be degraded by the action of any lenses. The efficiency here will be also >80yo. The bright-field contrast will be close to 100 /o efficient and will have a resolution determined by the ratio of elastic to inelastic scattering; that is, intermediate between 5 and 1 nm. EXPERIMENTAL RESULTS The array of detectors described above has been used in several investigations (Crewe et al., 1970; Lamvik, Isaacson & Crewe, 1973; Mall et al., 1973b) in our laboratory, and the results confirm expectations in all respects. Single heavy atoms supported on thin carbon films are readily visible using the annular detector alone (Wall et al., 1973a). Subtraction (electrically) of a fraction of the inelastic signal from the annular 256

11 Scanning transmission electron microscopy detector signal can be used to remove long-range structure in carbon films, making single heavy atoms even more visible. The reason that this is successful is that for a thin specimen of any given material the inelastic and elastic signals produce the same micrograph except that the resolution is poorer in the inelastic case. Subtraction is then equivalent to the use of an unsharp mask which can also be used to eliminate long-range order. Molecular weights of biological objects can be estimated by measuring the elastic and inelastic signals. Consider an object of unknown mass and Z. The total integrated elastic signal from the object is proportional to Z4I3. n, where n is the number of atoms and Z is the average atomic number. The total inelastic signal is proportional to Z1I3. n. So we have Total elastic CCZ~ ~~. Total inelastic ~ 482 3n. 20. These equations can be solved for Z and n. If we make the additional approximation that the atomic weight is twice the atomic number for biological objects the molecular weight can be estimated. This method could be improved in precision if more accurate cross-sections were known. MORE COMPLEX DETECTORS It is perhaps obvious that the detector array described above does not extract all the information which is available from the scattered electrons and that many other arrangements are possible for more specialized investigations. We mention a few possibilities below. (1) Annular detectors The single annular detector system only indicates the total number of elastically scattered electrons but gives no information about the angular distribution. Two or more annular detectors covering different angular ranges could provide this information. It is doubtful at the moment whether this information will ever be of much value. The reason for this is that the angular distributon as indicated by the value of 0, is only a slow function of Z. It is possible, however, that the use of a wide-angle detector would provide greater discrimination between low- and high-z materials. (2) Phase contrast Phase contrast is commonly used in conventional microscopy. We have previously shown that by using a very small detector which subtends an angle which is only a small fraction of 01, one can obtain such phase contrast. The efficiency is low, however, because a correspondingly small fraction of electrons are collected by the detector. Rose (1973a) has shown that the situation can be improved considerably by using two detectors within the cone of unscattered electrons. Using such a system of detectors the efficiency can be as high as 50,,. (3) Inelastic detectors By using a spectrometer capable of detecting only a narrow band of energy losses one can achieve high discrimination levels between otherwise similar materials. To do this one can take advantage of known energy loss spectra. This method would be particularly advantageous in metallurgical investigations where the details of energy-loss spectra in the range 0-50 V are known for several materials. 257

12 Albert V. Crewe Energy losses greater than 100 V can also be used. Such losses occur when X-ray excitation occurs and the energy loss spectrum consists of a sharp edge at the energy corresponding to the X-ray followed by a long tail which falls off hyperbolically. In current technology (microprobe analysers) the X-ray itself is detected and used for analytical purposes. However, it should be noted that the collecting power of X-ray detectors is small (- 1% or less), a fact which restricts spatial resolution because of the need for high currents and means that thick specimens must normally be used. It is possible, however, to design a spectrometer system which will collect looyo of the energy loss electrons with adequate resolving power. Such a system would undoubtedly allow one to improve spatial resolution and decrease the thickness of the specimen. CONCLUSION The STEM has only recently demonstrated that it is capable of high resolution, and to date only two such machines have operated at their theoretical resolutionboth in this laboratory. In view of this it would be fair to say that such machines have not been exploited fully. Their ultimate capabilities are neither as well known nor as well developed as the CEM. It seems probable that better and more versatile machines than ours will be built and that new contrast mechanisms will be invented for particular purposes. For example, we have not devoted any attention to the solution of metallurgical problems in our laboratory and have only recently begun to investigate thick biological specimens. Finally it should be mentioned that the STEM has some unique advantages which should be exploited. It is an ideal instrument on which to attempt the correction of lens aberrations since this can be performed on a mono-energetic and almost parallel beam, and we hope to attempt this in the near future. References Broers, A.N. (1973) High resolution thermionic cathode scanning transmission electron microscope. Appl. Phys. Lett. 22, No. 11, 610. Butler, J.W. (1966) Digital computer techniques in electron microscopy. Proc. 6th Znt. Congr. Electron Microsc. Kyoto, p Crewe, A.V. (1970a) The current state of high resolution scanning electron microscopy. Q. Rev. Biophys. 3, 137. Crewe, A.V. (1970b) Field emission and an electron gun, Microscope design using field emission and Contrast mechanisms in a high resolution scanning microscope. Lectures presented at Centre for Scientific Culture, Erice, Sicily. In: Electron Microscopy in Materials Science (Ed. by. U. Valdre) Academic press, New York. Crewe, A.V. (1972) Production of electron probes using a field emission source. In: Progress in Optics, Vol. 11. (Ed. by E. Wolf), pp North Holland, Amsterdam. Crewe, A.V., Eggenberger, D.N., Wall, J. & Welter, L.M. (1968) An electron gun using a field emission source. Rev..scient. Znstrum. 39, 4. Crewe, A.V., Langmore, J. & Wall, J. (1970) The visibility of single atoms. Science, N. Y. 168, 393. Crewe, A.V. & Retsky, M. (1972) A 100 kv scanning microscope. Proc. 30th Ann. Meeting, EMSA, p Crewe, A.V. & Wall, J. (1970) A scanning microscopc with 5 A resolution. J. molec. Biol. 48, 375. Haine, M.E. (1961) The Electron Microscope, p E. & F. Span Ltd, London. Haine, M.E. & Mulvey, T. (1954) The application and limitations of the edge diffraction test for astigmatism in the electron microscope. J. scient. Znstrum. 31, 325. Heidenreich, R. J. (1964) Fundamentals of Transmission Electron Microscopy. Interscience, New York. Isaacson, M. (1972) The interaction of 25 kev electrons with the nucleic acid bases adenine, thymine and uracil. J. chem. Phys. 56, 1803.

13 Scanning transmission electron microscopy Isaacson, M., Langmore, J. & Wall, J. (1974) Collection of scattered electrons in dark field electron microscopy. Optik, 38, 335. Lamvik, M., Isaacson, M. & Crewe, A.V. (1973) Studies of aggregates of two muscle proteins with scanning and conventional transmission electron microscopy. Proc. 31st Ann. Meeting, EMSA, p Lenz, F. (1954) Zur Streuung mittelschneller Elektronen in kleinste Winkel. Z. Nutur. 9a, 185. Rose, H. (1973a) Phase contrast in scanning transmission electron microscopy. Optik (to be published). Rose, H. (1973b) To what extent are inelastically scattered electrons useful in the STEM? Proc. 31st Ann. Meeting EMSA, p Wall, J., Langmore, J., Isaacson, M. & Crewe, A.V. (1973a) Scanning transmission electron microscopy at high resolution. Proc. Nutn. Acud. Sci., USA (to be published). Wall, J., Langmore, J., Isaacson, M. & Crewe, A.V. (1973b) Resolution attainable with the present day STEM. Proc. 31st Ann. Meeting EMSA, p Zeitler, E. & Thomson, M.G.R. (1970) Scanning transmission electron microscopy. Oprik, 31, 212,