2. Los Estados
2.1. Noción y elementos
I dare say that’s an idea which has already occurred to you, but with the weight of my great mind behind it, no doubt it strikes the imagination more forcibly. – Dorothy Sayers
T
here are several long-ranging effects of the work described in this report. My time with the CUORE experiment has allowed me to work on many different projects, and I consider it to be a remarkable and formative experience in my life. Professionally, the contributions that have been made are useful to CUORE, and ultimately the scientific community, but I have also personally gained from my work.While the background reduction techniques of the parylene test tower were not ultimately adopted by the collaboration, there are great prospects for the use of this style of background reduction in a future detector. I hope to have the chance to expand my ideas in other novel bolometric detectors.
The contributions made to the gluing machine are presently in place. The image recognition software may require moderate adjustments as the gluing hardware and associated processes evolve. The temperature stabilization system is now stable and operating.
The wire bonding procedures are now complete, and bonding of the towers is currently under- way. I will return to LNGS in July 2013 to bond a tower, making use of the manual that was written and the training I received.
The ability to be part of a collaborative endeavor of such a large-scale physics project has been very rewarding, and I hope to continue pursuing research goals in this field.
A. Current Standard Model
As a time capsule, the basic description of the Standard Model as of 2013 (updated 2000) is included here [30].
B. Signal Rate of CUORE
The derivation here is heavily inspired by an unpublished manuscript written by Thomas Gutier- rez [24].
A radioactive decay is described by a rate equation such that the change in number of ra- dioactive atoms is proportional to the number in existence at that moment. That is to say that
d
dt(N ) = −rN (B.1)
where r is the decay rate constant.1 The solution to this is trivial and can be found in any elementary differential equations text as
N (t) = N0e−rt (B.2)
where N0 is the initial population of radioactive atoms at time t = 0. As the exponent must have a dimensionless argument, it is easy to see that r has units of inverse time. It is convenient to characterize systems by a characteristic time constant τ (with units time), equal to 1r; this allows us to rewrite Equation B.2 as
N (t) = N0e−t/τ (B.3)
It is also often convenient to represent nuclear decays in terms of a half-life τ1
2, the amount of
time in which half of any continuously decaying sample will have decayed. This can be found very simply by presuming that at time t = τ1
2, N (t) = N0 2 , as N0 2 = N0e τ1 2/τ (B.4) Solving for τ1
2 then gives the half-life as
τ1
2 = τ ln 2. (B.5)
As the decay rates we deal with are exceptionally low, and rt = τt 1, it is valuable to take advantage of the ability to approximate this expression. The power series representation of e−αx in x is given as 1 − α x 1 1! + . . . (B.6) 1
You would be keen to note that this is a continuous equation describing a discrete process. Don’t worry – just apply it to a large enough sample and it won’t make a difference.
It is therefore reasonable to make the simplification that N = N0e−t/τ ≈ N0 1 − t τ . (B.7)
We will also define a quantity called signal, which is just the number of observed decays after time t. S = N0− N (B.8) = N0− N0 1 − t τ (B.9) = N0t τ (B.10)
The time constant τ then is just
τ = N0t
S (B.11)
Recalling our expression for the half-life in Equation B.5, we can then write the half-life in terms of the signal, τ1 2 = N0t S ln 2. (B.12)
We can rearrange this one last time to give us the expected signal as a function of the half life and initial population size
S = N0t τ1
2
!
ln 2. (B.13)
We can determine the mass of 130Te in CUORE using a simple argument. There will be 988 crystals, each weighing 750 g. of that mass, only a fraction is130Te.
N0 = (750 g) × (988 crystals) × 127.6 g Te 159.6 g TeO2 × 0.38 g 130Te g Te (B.14) = 225 kg (B.15)
We can convert this amount to a number of atoms of130Te using a simple conversion from grams to moles. This mass then gives us an N0 of (mT e× NA). Plugging this into our signal equation above, and recognizing that the half life of neutrinoless double-beta decay in130Te is of order 1025 years, gives us a signal of
S = 225 × 10 3 g130Te 1 130 mol/g130Te 6.02 × 1023 atoms/mol (1025yrs) ln 2 = 73 counts yr (B.16) or 1 count every 5 days. This signal is greater than the actual expected neutrinoless double-beta decay signal, as this would presume perfect counting efficiency. This is simply an upper limit.
C. Crystal Mass Reduction by Cleaning
Each CUORE crystal weighs approximately 750 g. The dimensions of each crystal are 5 cm3. The density of TeO2 is 6.04 g/cm3.
The etching and lapping procedures are designed to each remove 1g of material, making a total of 2g. Per face then, this is 26, or 13g.
The volume occupied by this mass can be expressed in two ways, as:
V = m
ρ = As,1D (C.1)
where m and ρ are the mass and density, As, 1 is the surface area of a single face, and D is the depth lost to the cleaning. We can then solve for D, as
D = m ρAs,1 (C.2) = 1 3 g × 1 cm3 6.04 g× 1 25 cm 2 (C.3) = 0.0022075 cm (C.4) = 22µm (C.5)
So, then each cleaning removes approximately 22 µm per face. This is potentially problematic for several reasons.
• Reduces active mass
• Potentially increases vibration, by not fitting in PTFE holders as well
If all of the 988 crystals were to undergo an extra cleaning, the active mass would be reduced by approximately 2 kg TeO2, the equivalent of losing 2-3 crystals.
The PTFE holders are manufactured to tight tolerances, and must be within ∼ 100µm of the specified value [31, pg. 17]. For some spacers, a reduction of 20 µm per face, or 40 µm in any given dimension, could be a large enough difference that the specified PTFE size is no longer correct, and the crystals may not be held firmly. Certainly, after multiple cleanings, the risk is increased. If the crystals are not held firmly, they can move, or vibrate; these vibrations may be picked up as signal, and can act as background as well.
D. Cleaning Techniques
In CUORE, there are several standard cleaning techniques, designed for efficient and ultra-high radiopurity of any detector component and everything that comes into contact with a detector component. I will outline here the techniques that are currently used for cleaning copper and PTFE, many of which have also been described by Luca Pattavina [32]. Virtually all the cleaning described takes place in a heated ultrasonic bath to increase efficiency of cleaning. Many of the techniques are inspired by those used in the semiconductor industry, and for this reason, there are several valuable texts in existence on the topic, such as [33].
D.1. Copper Cleaning
There are many copper parts used in CUORE, as the entire tower frame structure which holds the crystals is made of copper. A sample of the copper parts from one detector can be seen in Figure D.1.
Figure D.1.: The copper parts cleaned for the parylene test. Note that the frames at right have the female pins already glued in them.
The copper is first cleaned in a soap solution, using a 1% Micro 90 solution, placed in a polyethylene bag. This bag is then put into the heated ultrasonic bath for 20 minutes. The parts
are rinsed using high-purity water (∼ 18 MΩ-cm). The parts are then put into polyethylene bags containing 5% citric acid solution. Immediately before placing in the bath, “some” hydrogen peroxide is added – the amount depends on the parts being cleaned and the temperature of the bath, and is usually no more than 2%. For very small parts such as the wiring pins or bolts, the hydrogen peroxide may be omitted completely. These are placed in a bath for 20 minutes. The copper parts are then rinsed very thoroughly, and dried quickly using clean room wipers and nitrogen. The parts may be baked in a low-temperature oven for drying. After completely dry, the parts should be stored under vacuum.
D.2. PTFE Cleaning
The PTFE cleaning technique is principally very similar to the copper cleaning. The PTFE is first rinsed with ultrapure water. Next, it is cleaned using Micro 90 soap, again using a 1% solution, placed in a polyethylene bag. This bag is then put into the heated ultrasonic bath for 20 minutes. The soap can be poured from the bag, and the parts may be rinsed repeatedly in the bag, removing all traces of soap. Following the soap cleaning, a 5% nitric acid solution is prepared using high-purity nitric acid, and added until the parts are covered. This bag is then placed in the heated ultrasonic bath for 20 minutes. The waste acid is poured into the appropriate waste container, and the parts are rinsed thoroughly. A second nitric acid cleaning is performed, then the parts are rinsed and dried using nitrogen. The parts should be stored under vacuum, in rigid containers, so that the pressure of the vacuum bag does not bend or damage the PTFE parts.
D.3. Removal of Epoxy
NTDs and heaters are glued to crystals using an epoxy, and it is occasionally necessary to remove these devices from the crystal. There are two primary methods used for this, though if possible, it is best to never have to remove an NTD.
The first method is to use the solvent dichloromethane. Dichloromethane is relatively haz- ardous, so the appropriate procedures for use and disposal must be followed, as per an MSDS. It is notoriously difficult to dissolve epoxies, but in this case, it is possible to soften the epoxy by exposure to dichloromethane. As the cleanliness of the dichloromethane that we used was not well established, using the smallest amount possible is always recommended. The proposed mechanism is that, rather than actually dissolving the epoxy, the solvent fills the crosslinked polymer matrix, acting as something of a plasticizer and swelling the epoxy. This weakens the joint, making it possible to remove the epoxy. Practically, this is achieved by either pipetting a small amount onto the the glue, or by setting the crystal NTD-side down into a dish filled with dichloromethane. Pipetting should be tried first, and often removes the epoxy within minutes of application. It is less desirable to use a filled dish, as the solvent is very volatile and will evaporate quickly, reducing the potential for cleaning as well as exposing more of the crystal to the potentially dirty solvent, however, this allows the epoxy to be continually exposed for long periods of time.
the epoxy. Using a hot plate, the crystal may be set NTD-side down on the heated surface, briefly, until the epoxy is softened, usually within seconds. This should be done carefully and attentively, as it could create thermal stress in the crystal and cause it to crack.
Due to the hazardous nature of dichloromethane, it has been proposed that 2-methyltetrahydrofuran, a less hazardous solvent with similar properties, could be used in its place. Results of this are forthcoming.
E. Code
E.1. Glue Spot Image Recognition
The following Mathematica code is used for the image recognition described in Section 2.6.1.
(∗ : : Package : : ∗)
t o p P a t h = ”C: \ \ G l u e S p o t S c r i p t s \\ ”; p a t h=”C: \ \ Cuore \ Foto \\Temp\ Jenny \\ ”;
o u t F i l e = ”C: \ \ Cuore \ Foto \\Temp\ Jenny \\NTD Mask . j p g ”; i m a g e = Import[ path <> ” \\NTD. png ”] ;
n i n e s p o t = Import[ t o p P a t h <> ” / t e m p l a t e 2 . j p g ”] ;
S c a l e I m a g e [ img_ , sc_ ] := I m a g e R e s i z e [ img , I m a g e D i m e n s i o n s [ img ]∗ sc ] ; s c a l i n g = 0 . 5 ; i m a g e = S c a l e I m a g e [ image , s c a l i n g ] ; s p o t = S c a l e I m a g e [ spot , s c a l i n g ] ; n i n e s p o t = S c a l e I m a g e [ n i n e s p o t , s c a l i n g ] ; f i l t e r e d = I m a g e C o r r e l a t e [ image , n i n e s p o t , C o r r e l a t i o n D i s t a n c e , P e r f o r m a n c e G o a l −> ” Speed ”, P a d d i n g −> ” F i x e d ”] // C o l o r N e g a t e // I m a g e A d j u s t ;
(∗ mask g r a p h i c s f u n c t i o n p l o t s the mask ∗)
(∗ xc and yc are the x and y c o o r d i n a t e s o f c e n t e r c i r c l e o f mask ∗) (∗ opy i s the o p a c i t y o f the mask f o r a e s t h e t i c s ∗)
(∗ only standard 9 by 9 ∗) m a s k S t n d [ xc_ , yc_ , o p y _ ] :=
G r a p h i c s[ {
O p a c i t y [ opy ] , Red, Dotted , Thick ,
T ab le[ {
C i r c l e[ { ( xc − 1 − 1 \ [ Delta ] ) + ii +
ii \ [ Delta ] , ( yc − 1 − 1 \ [ Delta ] ) + jj + jj \ [ Delta ] } , r0 ] ,
C i r c l e[ { ( xc − 1 − 1 \ [ Delta ] ) + ii +
ii \ [ Delta ] , ( yc − 1 − 1 \ [ Delta ] ) + jj + jj \ [ Delta ] } , r0 + \ [ E p s i l o n ] ] } , { ii , 0 , 2 } , { jj , 0 , 2} ] } ] ; (∗ mask gra p h ic c o n t r u c t i o n ∗)
(∗ pre−tuned using another program ∗) p i n d = 1 ; (∗ known pin width i n mm ∗);
s p o t d = 0 . 9 ; (∗ expected spot c e n t e r to c e n t e r in mm ∗); (∗ pre−measured mask g l u e spot r a d i u s in p i x e l s ∗) (∗ r0 =25; ∗)
(∗ r0 =136/2; ∗) r0 = 8 2 . 6 / 2 ;
(∗ pre−measured mask pin diameters along with average in p i x e l s ∗) d1 = 1 1 6 ;
d2 = 1 1 6 . 3 ; d3 = 1 1 5 . 3 ;
a v g d 1 2 3 = ( 1 . ( d1 + d2 + d3 ) / 3 . ) ; m m 2 p i x e l s = a v g d 1 2 3 ;
(∗ c a l c u a t e d c a l i b r a t e d center −to−c e n t e r mask g l u e spot s e p a r a t i o n in \ p i x e l s ∗)
\ [ Delta ] = spotd ∗ avgd123 / pind ;
(∗ r a d i a l t o l e r a n c e r=r0 +\[ Epsilon ] in p i x e l s ∗) \ [ Epsilon ] = 5 ; \ [ Epsilon ] = 0 . 1∗ mm2pixels ; (∗ Finds Max ∗) Export[ o u t F i l e , Show[ { image , m a s k S t n d [ # [ [ 2 ] ] , # [ [ 1 ] ] , . 7 5 ] & / @ P o s i t i o n[ I m a g e D a t a [ I m a g e R e f l e c t @ f i l t e r e d ] , M a x @ I m a g e D a t a [ f i l t e r e d ] ] } ] ]
Here is a code snippet showing a more dense notation:
G [ i m a g e F i l e _ , t e m p l a t e G a u s s _ ] :=
Module[ { pinD , spotD , mm2pixels , mask , r0 , \ [ Delta ] , \ [ Epsilon ] , conv , image , pos , final , o u t F i l e } ,
p i n D = 1 ; s p o t D = 0 . 9 ;
m m 2 p i x e l s = ( 2 3 1 . 5 9 7 + 2 2 8 . 6 8 3 + 2 3 0 . 3 6 7 ) / 3 . ; r0 = 0 . 2 5∗ mm2pixels ;
\ [ Delta ] = spotD∗ mm2pixels / pinD ; \ [ Epsilon ] = 0 . 1∗ mm2pixels ; m a s k [ xc_ , yc_ , o p y _ ] :=
G r a p h i c s[ {
O p a c i t y [ opy ] , Red, Dashed , T h i c k n e s s[ 0 . 0 0 2 ] ,
T ab le[ {
C i r c l e[ { ( xc − 1 \ [ Delta ] ) + ii +
ii \ [ Delta ] , ( yc − 1 \ [ Delta ] ) + jj + jj \ [ Delta ] } , r0 ] ,
C i r c l e[ { ( xc − 1 \ [ Delta ] ) + ii +
ii \ [ Delta ] , ( yc − 1 \ [ Delta ] ) + jj + jj \ [ Delta ] } , r0 + \ [ E p s i l o n ] ]
} ,
{ ii , 0 , 2 } , { jj , 0 , 2} ]
} ] ; i m a g e = I f[ F i l e E x i s t s Q [ i m a g e F i l e ] , Import[ i m a g e F i l e ] , Quit[ ] ] ; c o n v = I m a g e A d j u s t @ C o l o r N e g a t e @ I m a g e C o r r e l a t e [ image , t e m p l a t e G a u s s , C o r r e l a t i o n D i s t a n c e , P e r f o r m a n c e G o a l −> ” Speed ”, P a d d i n g −> None] ;
pos = 0 . 5∗ ImageDimensions [ templateGauss ] +
F l a t t e n[ { # [ [ 1 ] ] , # [ [ 2 ] ] } & / @ {F l a t t e n[
# [ [ 1 ] ] & / @ {#} & / @ {P o s i t i o n[ I m a g e D a t a [ I m a g e R e f l e c t @ c o n v ] , M a x @ I m a g e D a t a [ c o n v ] ] } ] } ] ;
f i n a l = I m a g e @ S h o w [ { image ,
G r a p h i c s[ {Red, P o i n t[ { pos [ [ 2 ] ] , pos [ [ 1 ] ] } ] } ] , m a s k [ pos [ [ 2 ] ] , pos [ [ 1 ] ] , 0 . 5 ] } ] ; o u t F i l e = F i l e N a m e J o i n [ { D i r e c t o r y N a m e @ i m a g e F i l e , F i l e B a s e N a m e @ i m a g e F i l e <> ” Mv3 . 3 . ” <> F i l e E x t e n s i o n @ i m a g e F i l e } ] ;
Export[ outFile , final ] ]
E.2. Temperature Control
I wrote a simple python script to log data from the heater, in the temperature stabilization system, as described in Section 2.6.2. The code has been reproduced here:
# S e r i a l Data Temperature−L o g g e r
# Sam M e i j e r , w i t h m or al s u p p o r t o f Thomas O' Donnell # Thursday 23 Aug , 2012
# D e s c r i p t i o n :
# P r o d u c e s a f o r m a t t e d l i s t o f t e m p e r a t u r e v a l u e s o v e r time , t a k e n by # a PLC w i t h a s e r i a l o u t p u t . T h i s o u t p u t i s c o n v e r t e d t o USB w i t h a # c o n v e r t e r d o n g l e b e f o r e a c q u i s i t i o n .
# Time i s d i s p l a y e d i n UNIX time , t e m p e r a t u r e i s i n d e g r e e s C e l s i u s . # To a da pt f o r a machine r u n n i n g a d i f f e r e n t o p e r a t i n g system , t h e # ”pp” v a r i a b l e w i l l p r o b a b l y need t o be changed t o r e f l e c t t h e new # p o r t a s s i g n m e n t .
# OSX p o r t ='/dev/ t t y . u s b s e r i a l '
# Windows p o r t ='COM# ' , where # i s the c o r r e c t port number # ∗ nix p o r t ='/dev/ ttyS # ' , where # i s the c o r r e c t port number
from h e a d e r i m p o r t ∗ # s e e h e a d e r . py ## U s e r I n i t i a l i z a t i o n s : pp = ” / dev / t t y . u s b s e r i a l ” r u n t i m e = 1 0 ; # s e c o n d s # F i l e h a n d l i n g s e t u p f N a m e = f i l e F i n d e r ( ) e r r N a m e = ”%s%s ” % (” E r r o r ”f n a m e )
f C a l l = ”%s %s ” % (” . / RPlot ”, fName ) p r i n t ” S a v i n g t o : %s \n” % ( fName ) # S e r i a l communication s e t u p t r y: ser = s e r i a l . S e r i a l ( p o r t=pp , b a u d r a t e =4800 , t i m e o u t =3 , b y t e s i z e =8 , p a r i t y='O ', r t s c t s =1 , s t o p b i t s =2) e x c e p t: p r i n t ” E r r o r : Problem w i t h s e r i a l p o r t ! ” p r i n t ” Ensure d e v i c e i s c o n n e c t e d c o r r e c t l y and c o r r e c t p o r t i s c h o s e n . ”
p r i n t ” C u r r e n t l y , you' re attempting to read from '% s ' , which f a i l e d . ” % ( pp )
p r i n t ” B e t t e r l u c k n e x t t i m e . . . ” sys . e x i t ( 0 ) # Main t h i n g s s t a r t T i m e = t i m e . t i m e ( ) f i n i s h T i m e = s t a r t T i m e + r u n t i m e w h i l e t i m e . t i m e ( ) < f i n i s h T i m e : out = ser . r e a d ( 9 ) out = re . s e a r c h ( r” \S∗\ s ∗(\ S ∗) ”, out ) # f o r m a t t i n g out = out . g r o u p ( 1 ) # f o r m a t t i n g t r y: out = f l o a t ( out ) # p r e v e n t s ”V01” e r r o r −r e a d t = t i m e . t i m e ( ) p r i n t t , out
s a v e r ( f i l e=fName , t e m p=out , t i m e=t )
e x c e p t: p r i n t ” S e r i a l r e a d e r r o r , s k i p p i n g . . . ” s a v e r ( f i l e=errName , t e m p=” E r r o r r e a d i n g ”, time=t ) p a s s t i m e . s l e e p ( . 5 ) # w a i t t i m e ( i n s ) t o s c a r e o f f e r r o r s ser . f l u s h I n p u t ( ) # c l e a r b u f f e r on d e v i c e p r i n t ”Run c o m p l e t e d a t : ” s t r f t i m e (” %a , %d %b %Y %H:%M:%S”, l o c a l t i m e ( ) ) ser . c l o s e ( ) # c l o s e p o r t #r o o t e r ( f C a l l )
This code relies on a header, which I also wrote, given here:
i m p o r t s e r i a l # s e r i a l d a t a comm i m p o r t t i m e # f o r time−s t a m p i n g i m p o r t sys # s y s t e m commands i m p o r t re # r e g u l a r e x p r e s s i o n i m p o r t os # f o r s y s t e m c a l l s i m p o r t c o m m a n d s # f o r s y s t e m c a l l s from t i m e i m p o r t gmtime , s t r f t i m e , l o c a l t i m e i m p o r t e a s y g u i as gui # g u i c o n t r o l # F u n c t i o n D e f i n i t i o n s d e f f i l e F i n d e r ( ) : ” D e t e r m i n e s which f i l e t o w r i t e t o ” t r y: f u l l = t i m e . g m t i m e ( t i m e . t i m e ( ) ) yr = f u l l . t m _ y e a r
m o n t h = f u l l . t m _ m o n day = f u l l . t m _ m d a y h o u r = f u l l . t m _ h o u r min = f u l l . t m _ m i n sec = f u l l . t m _ s e c
f N a m e = ”%s %s %s %s %s %s . l o g ” % ( yr , month , day , hour , min , sec )
e x c e p t: f N a m e = ” l o g 1 . l o g ” p r i n t ” E r r o r c h o o s i n g u n i q u e l o g name , s e t t i n g t o d e f a u l t . ” r e t u r n ”%s%s ” %(” l o g s / ”, fName ) d e f s a v e r ( file , time , t e m p ) : ” S a v e s d a t a p o i n t t o l o g f i l e ” f = o p e n ( file , ” a ”) o u t S t r = ” %3.2 f %3.1 f \n” % ( time , temp ) f . w r i t e ( str ( o u t S t r ) ) f . c l o s e r e t u r n d e f r o o t e r ( c a l l ) : ” Opens r o o t p l o t ” r e t u r n
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[28] XKCD, “Python,” 2013. http://xkcd.com/353/. 33
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[30] Contemporary Physics Education Project, “Standard Model Poster.” 38
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