Hi,
I will outline a typical crystal specification I use. Just a note first that I am a radio technician, (to component level) by trade and I also order crystals for personal use. Sometimes I have to work out the crystal specification from measurements on an original crystal, but thats another thread.
The specifications are pretty basic, but one doesnt need to over specify.
I will add some notes where applicable
(1)Frequency to 10 Hz. (Or 1 Hz at HF)
(2)Type of Cut. The most common is probably AT cut. For very high specification
oscillators such as OCXO, then SC cut. SC cut is normally more expensive and typically operated in an oven at elevated temperature
(3) Fundamental or overtone. Most generic type crystals for use up to 35 MHz or so are fundamental, but at higher frequencies odd order vibrational harmonics (overtone) are selected by the oscillator design. These may extend up to 9th in some cases but the crystal overtone must be specified. Typically for 100 MHz crystals the fifth overtone is selected. Note also that some high spec crystals at HF use an overtone mode
(4)The type of holder, and connections need to be specified. This can be downloaded from most crystal manufacturers websites. For wire-in crystals of ~12mm height, this is the HC49/U holder. The most common method of sealing these is resistance-weld. Although cold-weld is probably still available if one hunts around. Solder weld should not be used.
SMD packages are available, and are commonly used in modern equipment.
(4) Temperature range. This is typically -10 to +60C for room temperature use, with calibration done at ~ 25C. If using this type of crystal then one must specify the crystal frequency tolerance over the temperature range. This is normally in +/-ppm (Parts per million) A value of +/-10 ppm is typical, and one can select that from crystal manufacturers info.
If one is selecting a crystal for oven use, then an elevated temperature is selected depending on the application. For amateur type designs 60C is quite good (This elevated temperature is normally noted as the turnover temperature). Note that cutting of crystals for these exact temeperatures is very difficult, so some adjustment is normally available in the oven temperature of the OCXO to fine tune the turnover.
(5) The calibration accuracy is a specification where the crystal will sit when operating at its nominal temperature and correct load. Again in +/- ppm. 5 or 10 ppm is typical
(6) Load. For most HF crystals they are specified with a capacitive load such as 32 pF. The oscillator must present the correct load to crystal, for the crystal to operate on the correct frequency.
A crystal can operate in a series type circuit with, or without load capacitance. (Specify C-load value or Series resonance) Most overtone crystals are specified as series resonance, however they can be specified also with load capacity depending on the circuit
(7) Preaged. Typically specified in +/- ppm/year. About +/- 1 ppm is acheivable at low cost, using accelerated aging techniques by the crystal manufacturers. Otherwise wait for a year or more, to slow down. If you have a leaking crystal it doesnt slow down. (Been there, done that)
(8) ESR. (Equivalent series resistance) For 5th overtone crystals around 100 MHz, 30 to 35 ohms is acheivable and 3rd overtone are around 10 to 20 ohms.
I dont usually order HF crystals, but one can sometimes specify approximate motional parameters if needed fo specific applications.
(Google search Cliftonlaboratories and crystal and he shows some basic tests on crystals with which motional parameters can be derived)
The crystals I get, also have some of the motional parameter info, in the data when received, and typical unloaded Q factors of 70,000-100,000 for overtone VHF crystals have been calculated. For HF crystals this can be significantly higher and values of just below 1 Million have been seen calculated from high quality German KVG crystals around 2.5 MHz. Note it is very easy to throw away such performance in simple circuits.
I think I covered most items with a general note. When ordering I normally create a list of these parameters for each crystal and put each item of info in. Double check the frequency as it easy to put numbers in the wrong order, or miscalculate
If you are unsure when ordering a crystal, talk to (or email) the crystal manufacturer or ask questions of others and research. One can never stop learning.
Hope that is of some help
Kevin ZL1UJG